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MAT 540 Quantitative Methods

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Assignments:

Week 3 Assignment 1: JET Copies Case Problem

Read the “JET Copies” Case Problem on pages 678-679 of the text. Using
simulation estimate the loss of revenue due to copier breakdown for one year, as
follows:
   1.     In Excel, use a suitable method for generating the number of days needed
        to repair the copier, when it is out of service, according to the discrete
        distribution shown.
   2.     In Excel, use a suitable method for simulating the interval between
        successive breakdowns, according to the continuous distribution shown.
   3.     In Excel, use a suitable method for simulating the lost revenue for each day
        the copier is out of service.
   4.     Put all of this together to simulate the lost revenue due to copier
        breakdowns over 1 year to answer the question asked in the case study.
   5.     In a word processing program, write a brief description/explanation of how
        you implemented each component of the model. Write 1-2 paragraphs for
        each component of the model (days-to-repair; interval between breakdowns;
        lost revenue; putting it together).
   6.     Answer the question posed in the case study. How confident are you that
        this answer is a good one? What are the limits of the study? Write at least
        one paragraph.
Week 4 Assignment 2: Internet Field Trip - Forecasting Methods

1.    Research: Research at least six (6) information sources on forecasting
methods; take notes and record and interpret significant facts, meaningful
graphics, accurate sounds and evaluated alternative points of view.
2.    Preparation: Produce as storyboard with thumbnails of at least ten (10)
slides. Include the following elements:
        Title of slide, text, background color, placement & size of graphic, fonts -
color, size, type for text and headings
        Hyperlinks (list URLs of any site linked from the slide), narration text, and
audio files (if any)
o Number on slides clear
o Logical sequence to the presentation
3.    Content: Provide written content with the following elements:
o introduction that presents the overall topic (clear sense of the project’s main
idea) and draws the audience into the presentation with compelling questions or
by relating to the audience's interests or goals.
o accurate, current
o clear, concise, and shows logical progression of ideas and supporting
information
o motivating questions and advanced organizers
o drawn mainly from primary sources
4.    Text Elements: Slides should have the following characteristics:
o fonts are easy-to-read; point size that varies appropriately for headings and
text
o italics, bold, and indentations enhance readability
o background and colors enhance the readability of text
o appropriate in length for the target audience; to the point
5.    Layout: The layout should have the following characteristics:
o visually pleasing
o contributes to the overall message
o appropriate use of headings, subheadings and white space
6.    Media: The graphics, sound, and/or animation should
o assist in presenting an overall theme and enhance understanding of concept,
ideas and relationships
o have original images that are created using proper size and resolution;
enhance the content
o have a consistent visual theme.
7.    Citations: The sources of information should:
o properly cited so that the audience can determine the credibility and authority
of the information presented
o be properly formatted according to APA style



Week 7 Assignment 3 Case Problem - Julia’s Food Booth

Julia is a senior at Tech, and she’s investigating different ways to finance her final
year at school. She is considering leasing a food booth outside the Tech stadium at
home football games. Tech sells out every home game, and Julia knows, from
attending the games herself, that everyone eats a lot of food. She has to pay $1,000
per game for a booth, and the booths are not very large. Vendors can sell either food
or drinks on Tech property, but not both. Only the Tech athletic department
concession stands can sell both inside the stadium. She thinks slices of cheese
pizza, hot dogs, and barbecue sandwiches are the most popular food items among
fans and so these are the items she would sell.

Most food items are sold during the hour before the game starts and during half time;
thus it will not be possible for Julia to prepare the food while she is selling it. She
must prepare the food ahead of time and then store it in a warming oven. For $600
she can lease a warming oven for the six-game home season. The oven has 16
shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three
food items before the game and then again before half time.

Julia has negotiated with a local pizza delivery company to deliver 14-inch cheese
pizzas twice each game – 2 hours before the game and right after the opening
kickoff. Each pizza will cost her $4.50 and will include 6 slices. She estimates it will
cost her $0.50 for each hot dog and $1.00 for each barbecue sandwich if she makes
the barbecue herself the night before. She measured a hot dog and found it takes
up about 16 in2 of space, whereas a barbecue sandwich takes up about 25 in2. She
plans to sell a piece of pizza for $1.50 and a hot dog for $1.60 each and a barbecue
sandwich for $2.25. She has $1,500 in cash available to purchase and prepare the
food items for the first home game; for the remaining five games she will purchase
her ingredients with money she has made from the previous game.

Julia has talked to some students and vendors who have sold food at previous
football games at Tech as well as at other universities. From this she has
discovered that she can expect to sell at least as many slices of pizza as hot dogs
and barbecue sandwiches combined. She also anticipates that she will probably sell
at least twice as many hot dogs as barbecue sandwiches. She believes that she will
sell everything she can stock and develop a customer base for the season if she
follows these general guidelines for demand.

If Julia clears at least $1,000 in profit for each game after paying all her expenses,
she believes it will be worth leasing the booth.

A. Formulate a linear programming model for Julia that will help you to advise her if
she should lease the booth. Formulate the model for the first home game. Explain
how you derived the profit function and constraints and show any calculations that
allow you to arrive at those equations.

B. Solve the linear programming model using a computer for Julia that will help you
advise her if she should lease the booth. In this solution, determine the number of
pizza slices, hot dogs and barbecue sandwiches she should sell at each game. Also
determine the revenues, cost and profit; and do an analysis of how much money she
actually will make each game given the expenses of each game.

Do an analysis of the profit solution and what impact it has on Julia’s ability to have
sufficient funds for the next home game to purchase and prepare the food. What
would you recommend to Julia?

C. If Julia were to borrow some money from a friend before the first game to
purchase more ingredients, she feels she can increase her profits. What amount, if
any, would you recommend to Julia to borrow?

D. Food prices have been rising lately. Assume purchase costs for the food is now
$6.00 for each pizza, $0.75 for each hot dog, and $1.25 for each barbecue
sandwich. Repeat the analysis of Part B. What would you recommend to Julia to do
at this point?
E. Julia seems to be basing her analysis on the assumptions that everything will go
as she plans. What are some of the uncertain factors in the model that could go
wrong and adversely affect Julia’s analysis? Given these uncertainties and the
results in (B), (C), and (D), what do you recommend that Julia do? Take into
consideration her profit margin for each game.




Week 10 Assignment 4 Case Problem - Stateline Shipping and Transport
Company

Read the “Stateline Shipping and Transport Company” Case Problem on pages 273-
274 of the text. Analyze this case, as follows:
1.    In Excel, or other suitable program, develop a model for shipping the waste
directly from the 6 plants to the 3 waste disposal sites.
2.    Solve the model you developed in #1 (above) and clearly describe the results.
3.    In Excel, or other suitable program, Develop a transshipment model in which
each of the plants and disposal sites can be used as intermediate points.
4.     Solve the model you developed in #3 (above) and clearly describe the results.
5.    Interpret the results and draw conclusions that address the question posed in
the case problem. What are the limits of the study? Write at least one paragraph.

There are two deliverables for this Case Problem, 1)the Excel spreadsheet, with the
different solutions given in separate worksheets, and 2) an accompanying written
description/explanation (submitted as a Word document). Please submit both of
them electronically via the drop box.


Discussion Questions:

Week 2:

       What are some benefits of using decision trees? In what ways can
       decision trees be used for business decisions? Name some real-world
       examples.

       How does the science of probability affect decisions? Why?

Week 3:

       Why do we use pseudorandom numbers in simulations? How do
       pseudorandom numbers affect the accuracy of a simulation?

       What is the role of statistical analysis in simulation?
Week 4:

      Choose one of the forecasting methods and explain the rationale behind
      using it in real-life. Describe how a domestic fast food chain with plans for
      expanding into China would be able to use a forecasting model.

      What is the difference between a causal model and a time- series
      model? Give an example of when each would be used. What are some of
      the problems and drawbacks of the moving average forecasting model?
      How do you determine how many observations to average in a moving
      average model? How do you determine the weightings to use in a
      weighted moving average model?

Week 6:

      What are some business uses of a linear programming model? Provide
      an example.

      In the graphical method, how do you know when a problem is infeasible,
      unbounded, or when it has multiple optimal solutions? What are the
      essential ingredients of an LP model? Why is it helpful to understand the
      characteristics of LP models?

      Not very many real world examples use only two variables, and those
      that do can usually be solved much more easily by guess and check
      methods rather than LP models. Why then do we study the graphical
      method? Be specific.

      Distinguish between a minimization and maximization LP model. How do
      you know which of these to use for any given problem?

      Give examples of both a minimization LP model and a maximization LP
      model. Every minimization model has a related maximization model. In
      what way do you think they are related?

Week 7:

      What does the shadow price reflect in a maximization problem? Please
      explain. How do the graphical and computer-based methods of solving LP
      problems differ? In what ways are they the same? Under what
      circumstances would you prefer to use the graphical approach?

      How does sensitivity analysis affect the decision making process? How
      could it be used by managers?
      In many ways, shadow prices are far more important results of an LP
      model then the optimal solution. Explain. Make sure that your answer
      provides context to the nature and utility of shadow prices.




Week 8:

      What is the relationship between decision variables and the objective
      function? What is the difference between an objective function and a
      constraint?

      Does the linear programming approach apply the same way in different
      applications? Explain why or why not using examples.

      Many LP models can be viewed through the lens of a Transpotation
      model. Choose one of the following types of problem and explain how to
      see it as a Transportation problem. That is, explain what the "goods" we
      are shipping are, what the "roads" we are shipping along are, what the
      costs of "shipping" are, what the supply" and "demand" are:


Week 9:

     Explain how the applications of Integer programming differ from those of linear
      programming. Why is “rounding-down” an LP solution a suboptimal way to solve
      Integer programming problems?


     Explain the characteristics of integer programming problems. Give specific
      instances in which you would use an integer programming model rather than an
      LP model. Provide real-world examples.


     Do you think Integer Programming or Linear Programming has more real world
      applications? Why? If Integer Programming is more prevalent, why do we focus
      so much on Linear Programming in this course? If Linear Programming is more
      prevalent, what do you think the challenges are facing Linear Programmers (since
      software like QM can handle all the computations)?


     Explain the characteristics of integer programming problems. Give specific
      instances in which you would use an integer programming model rather than an
      LP model. Provide real-world examples.
Quizzes:

Week 1 Quiz 1:

  1.    Which of the following is incorrect with respect to the use of models in
       decision making?
  2.    The probabilities of mutually exclusive events sum to zero.
  3.    The term decision analysis refers to testing how a problem solution
       reacts to changes in one or more of the model parameters.
  4.    Variable costs are independent of volume and remain constant.
  5.    A frequency distribution is an organization of numerical data about the
       events in an experiment.
  6.    Objective probabilities that can be stated prior to the occurrence of an
       event are
  7.    A set of events is collectively exhaustive when it includes _______ the
       events that can occur in an experiment.
  8.    Which of the following is not an alternative name for management
       science?
  9.    Which of the following is an equation or an inequality that expresses a
       resource restriction in a mathematical model?

  10. ____________ techniques include uncertainty and assume that there can
     be more than one model solution.

  11. A ___________ probability is the probability that two or more events that
     are not mutually exclusive can occur simultaneously.
  12. Total cost equal the fixed cost plus the variable cost per unit divided by
     volume.
  13. Profit is the difference between total revenue and total cost.
  14. The events in an experiment are mutually exclusive if only one can occur
     at a time.
  15. In a given experiment, the probabilities of all mutually exclusive events
     sum to one.
  16. An experiment is an activity that results in one of several possible
     outcomes.
  17. Fixed costs depend on the number of items produced.
  18. The steps of the scientific method are:
  19. A model is a functional relationship and include:
  20. In a given experiment the probabilities of mutually exclusive events sum to


Week 3 Quiz 2:

  1.    The coefficient of optimism is a measure of the decision maker's
       optimism.
  2.   A payoff table is a means of organizing a decision situation, including the
     payoffs from different decisions given the various states of nature.
  3. The maximin criterion results in the maximum of the minimum payoffs.
  4. A state of nature is an actual event that may occur in the future.
  5. The ______________ minimizes the maximum regret.
  6. The maximin criterion results in the
  7. A dominant decision is one that has better payoff than another decision
     under each state of nature.
  8. The maximin approach to decision making refers to
  9. The maximax criterion results in the maximum of the minimum payoffs.
  10. Determining the worst payoff for each alternative and choosing the
     alternative with the best worst is called
  11. The Hurwicz criterion is a compromise
  12. The maximax criterion results in the
  13. Regret is the difference between the payoff from the best decision and all
     other decision payoffs.
  14. Regret is the difference between the payoff from the
  15. The minimax regret criterion
  16. The Hurwicz criterion is a compromise between the maximax and
     maximin criteria.
  17. The term opportunity loss is most closely related to
  18. The equal likelihood criterion multiplies the decision payoff for each state
     of nature by an equal weight.
  19. The basic decision environment categories are
  20. Expected opportunity loss is the expected value of the regret for each
     decision.


Week 5 Quiz 3:

  1.    The terms in the objective function or constraints are not additive.
  2.    A feasible solution violates at least one of the constraints.
  3.    Which of the following could not be a linear programming problem
       constraint?
  4.    In a linear programming problem, a valid objective function can be
       represented as
  5.    Non-negativity constraints restrict the decision variables to negative
       values.
  6.    A graphical solution is limited to linear programming problems with
  7.    A constraint is a linear relationship representing a restriction on decision
       making.
  8.    Linear programming is a model consisting of linear relationships
       representing a firm's decisions given an objective and resource
       constraints.
  9.    Non-negativity constraints
  10. Decision models are mathematical symbols representing levels of
     activity.
  11. Which of the following could be a linear programming objective function?
  12. Decision variables
  13. A linear programming model consists of decision variables, constraints,
     but no objective function.
  14. The region which satisfies all of the constraints in a graphical linear
     programming problem is called the
  15. The _______________ property of linear programming models indicates
     that the decision variables cannot be restricted to integer values and can
     take on any fractional value.
  16. The production manager for the Coory soft drink company is considering
     the production of 2 kinds of soft drinks: regular and diet. Two of the limited
     resources are production time (8 hours = 480 minutes per day) and syrup
     limited to 675 gallons per day. To produce a regular case requires 2
     minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3
     gallons of syrup. Profits for regular soft drink are $3.00 per case and
     profits for diet soft drink are $2.00 per case. What is the time constraint?
  17. Cully furniture buys 2 products for resale: big shelves (B) and medium
     shelves (M). Each big shelf costs $500 and requires 100 cubic feet of
     storage space, and each medium shelf costs $300 and requires 90 cubic
     feet of storage space. The company has $75000 to invest in shelves this
     week, and the warehouse has 18000 cubic feet available for storage.
     Profit for each big shelf is $300 and for each medium shelf is $150. What
     is the objective function?
  18. In a linear programming model, the numberof constraints must be less
     than the number of decision variables.
  19. Proportionality means the slope of a constraint or objective function line is
     not constant.
  20. The objective function is a linear relationship reflecting the objective of an
     operation.


Week 6 Quiz 4:

  1.   The standard form for the computer solution of a linear programming
     problem requires all variables to the right and all numerical values to the
     left of the inequality or equality sign
  2. _________ is maximized in the objective function by subtracting cost
     from revenue.
  3. A croissant shop produces 2 products: bear claws (B) and almond filled
     croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of
     yeast, and 2 TS of almond paste. An almond filled croissant requires 3
     ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The
     company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of
     almond paste available for today's production run. Bear claw profits are 20
   cents each, and almond filled croissant profits are 30 cents each. What is
   the optimal daily profit?
4. In an unbalanced transportation model, supply does not equal demand
   and supply constraints have signs.
5. The production manager for Liquor etc. produces 2 kinds of beer: light
   and dark. Two of his resources are constrained: malt, of which he can get
   at most 4800 oz per week; and wheat, of which he can get at most 3200
   oz per week. Each bottle of light beer requires 12 oz of malt and 4 oz of
   wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat.
   Profits for light beer are $2 per bottle, and profits for dark beer are $1 per
   bottle. What is the objective function?
6. In a media selection problem, the estimated number of customers
   reached by a given media would generally be specified in the
   _________________. Even if these media exposure estimates are
   correct, using media exposure as a surrogate does not lead to
   maximization of ______________.
7. The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar
   (V). He has a limited amount of the 3 ingredients used to produce these
   chips available for his next production run: 4800 ounces of salt, 9600
   ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2
   ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a
   bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2
   ounces of herbs. Profits for a bag of Lime chips are $0.40, and for a bag of
   Vinegar chips $0.50. Which of the following is not a feasible production
   combination?
8. When formulating a linear programming model on a spreadsheet, the
   measure of performance is located in the target cell.
9. In a balanced transportation model, supply equals demand such that all
   constraints can be treated as equalities.
10. In a media selection problem, instead of having an objective of
   maximizing profit or minimizing cost, generally the objective is to maximize
   the audience exposure.
11. ____________ solutions are ones that satisfy all the constraints
   simultaneously.
12. The production manager for the Softy soft drink company is considering
   the production of 2 kinds of soft drinks: regular and diet. Two of her
   resources are constraint production time (8 hours = 480 minutes per day)
   and syrup (1 of her ingredient) limited to 675 gallons per day. To produce
   a regular case requires 2 minutes and 5 gallons of syrup, while a diet case
   needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are
   $3.00 per case and profits for diet soft drink are $2.00 per case. What is
   the optimal daily profit?
13. Determining the production quantities of different products manufactured
   by a company based on resource constraints is a product mix linear
   programming problem.
  14. When using linear programming model to solve the "diet" problem, the
     objective is generally to maximize profit.
  15. Profit is maximized in the objective function by
  16. Linear programming model of a media selection problem is used to
     determine the relative value of each advertising media.
  17. Media selection is an important decision that advertisers have to make. In
     most media selection decisions, the objective of the decision maker is to
     minimize cost.
  18. The dietician for the local hospital is trying to control the calorie intake of
     the heart surgery patients. Tonight's dinner menu could consist of the
     following food items: chicken, lasagna, pudding, salad, mashed potatoes
     and jello. The calories per serving for each of these items are as follows:
     chicken (600), lasagna (700), pudding (300), salad (200), mashed
     potatoes with gravy (400) and jello (200). If the maximum calorie intake
     has to be limited to 1200 calories. What is the dinner menu that would
     result in the highest calorie in take without going over the total calorie limit
     of 1200.
  19. In a multi-period scheduling problem the production constraint usually
     takes the form of :
  20. A constraint for a linear programming problem can never have a zero as
     its right-hand-side value.


Week 9 Quiz 5:

  1.     In a _______ integer model, some solution values for decision variables
       are integer and others can be non-integer.
  2.     In a total integer model, some solution values for decision variables are
       integer and others can be non-integer.
  3.     In a problem involving capital budgeting applications, the 0-1 variables
       designate the acceptance or rejection of the different projects.
  4.     If a maximization linear programming problem consist of all less-than-or-
       equal-to constraints with all positive coefficients and the objective function
       consists of all positive objective function coefficients, then rounding down
       the linear programming optimal solution values of the decision variables
       will ______ result in a(n) _____ solution to the integer linear programming
       problem.
  5.     The branch and bound method of solving linear integer programming
       problems is an enumeration method.
  6.     In a mixed integer model, all decision variables have integer solution
       values.
  7.     For a maximization integer linear programming problem, feasible solution
       is ensured by rounding _______ non-integer solution values if all of the
       constraints are less-than -or equal- to type.
  8.     In a total integer model, all decision variables have integer solution
       values.
  9. The 3 types of integer programming models are total, 0 - 1, and mixed.
  10. The branch and bound method of solving linear integer programming
     problems is ________________.
  11. The linear programming relaxation contains the _______ and the original
     constraints of the integer programming problem, but drops all integer
     restrictions.
  12. The branch and bound method can only be used for maximization integer
     programming problems.
  13. The solution value (Z) to the linear programming relaxation of a
     minimization problem will always be less than or equal to the optimal
     solution value (Z) of the integer programming minimization problem
  14. The implicit enumeration method
  15. Types of integer programming models are _____________.
  16. In a 0 - 1 integer model, the solution values of the decision variables are 0
     or 1.
  17. Which of the following is not an integer linear programming problem?
  18. In a mixed integer model, some solution values for decision variables are
     integer and others can be non-integer.
  19. Rounding small values of decision variables to the nearest integer value
     causes ______________ problems than rounding large values.
  20. In using rounding of a linear programming model to obtain an integer
     solution, the solution is


Week 6 Midterm Exam:

  1.   ___________ is a technique for selecting numbers randomly from a
     probability distribution.
  2. Monte Carlo is a technique for selecting numbers randomly from a
     probability distribution.
  3. Analogue simulation replaces a physical system with an analogous
     physical system that is _____________ to manipulate.
  4. Variable costs are independent of volume and remain constant.
  5. Regret is the difference between the payoff from the best decision and all
     other decision payoffs.
  6. The maximin criterion results in the
  7. A payoff table is a means of organizing a decision situation, including the
     payoffs from different decisions given the various states of nature.
  8. In a weighted moving average, weights are assigned to most
     __________ data.
  9. The maximin criterion results in the maximum of the minimum payoffs.
  10. A state of nature is an actual event that may occur in the future.
  11. Which of the following is not an alternative name for management
     science?
  12. A _________ period of real time is represented by a __________ period
     of simulated time.
13. Simulation results will not equal analytical results unless ___________
   trials of the simulation have been conducted to reach steady state.
14. The minimax regret criterion
15. Objective probabilities that can be stated prior to the occurrence of an
   event are
16. Which of the following is incorrect with respect to the use of models in
   decision making?
17. The steps of the scientific method are:
18. A seasonal pattern is an up-and-down repetitive movement within a trend
   occurring periodically.
19. The maximax criterion results in the
20. ____________ techniques include uncertainty and assume that there can
   be more than one model solution.
21. The maximax criterion results in the maximum of the minimum payoffs.

22. Regret is the difference between the payoff from the
23. A long period of real time is represented by a short period of simulated
   time.
24. A trend is a gradual, long-term, up or down movement of demand.
25. ____________ use management judgment, expertise, and opinion to
   make forecasts.
26. ____________ moving averages react more slowly to recent demand
   changes than do ____________ moving averages.
27. In computer mathematical simulation a system is replicated with a
   mathematical model that is analyzed.
28. Which of the following is an equation or an inequality that expresses a
   resource restriction in a mathematical model?

29. Analogue simulation replaces a physical system with an analogous
   physical system that is easier to manipulate.

30. An experiment is an activity that results in one of several possible
   outcomes.

31. Random numbers are equally likely to occur.
32. An example of forecasting is
33. The ______________ minimizes the maximum regret.
34. ____________ is an up-and-down repetitive movement in demand.
35. It's often ____________ to validate that the results of a simulation truly
   replicate reality.
36. A short period of real time is represented by a long period of simulated
   time.
37. In computer mathematical simulation, a system is replicated with a
   mathematical model that is analyzed with the computer.
38. A cycle is an up-and-down repetitive movement in demand.
39. Profit is the difference between total revenue and total cost.
40. A model is a functional relationship and include:
Week 11 Final Exam:

  1.   Which of the following could be a linear programming objective function?
  2.   Which of the following could not be a linear programming problem
     constraint?
  3. Types of integer programming models are _____________
  4. The production manager for Beer etc. produces 2 kinds of beer: light (L)
     and dark (D). Two resources used to produce beer are malt and wheat.
     He can obtain at most 4800 oz of malt per week and at most 3200 oz of
     wheat per week respectively. Each bottle of light beer requires 12 oz of
     malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8
     oz of wheat. Profits for light beer are $2 per bottle, and profits for dark
     beer are $1 per bottle. If the production manager decides to produce of 0
     bottles of light beer and 400 bottles of dark beer, it will result in slack of
  5. The reduced cost (shadow price) for a positive decision variable is 0
  6. Decision variables
  7. A plant manager is attempting to determine the production schedule of
     various products to maximize profit. Assume that a machine hour
     constraint is binding. If the original amount of machine hours available is
     200 minutes., and the range of feasibility is from 130 minutes to 340
     minutes, providing two additional machine hours will result in the
  8. Decision models are mathematical symbols representing levels of
     activity.
  9. The integer programming model for a transportation problem has
     constraints for supply at each source and demand at each destination.
  10. In a transportation problem, items are allocated from sources to
     destinations
  11. In a media selection problem, the estimated number of customers
     reached by a given media would generally be specified in the
     _________________. Even if these media exposure estimates are
     correct, using media exposure as a surrogate does not lead to
     maximization of ______________.
  12. ____________ solutions are ones that satisfy all the constraints
     simultaneously.
  13. In a linear programming problem, a valid objective function can be
     represented as
  14. The standard form for the computer solution of a linear programming
     problem requires all variables to the right and all numerical values to the
     left of the inequality or equality sign
  15. Constraints representing fractional relationships such as the production
     quantity of product 1 must be at least twice as much as the production
     quantity of products 2, 3 and 4 combined cannot be input into computer
     software packages because the left side of the inequality does not consist
     of consists of pure numbers.
16. In a balanced transportation model where supply equals demand
17. The objective function is a linear relationship reflecting the objective of an
   operation.
18. The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar
   (V). He has a limited amount of the 3 ingredients used to produce these
   chips available for his next production run: 4800 ounces of salt, 9600
   ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2
   ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a
   bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2
   ounces of herbs. Profits for a bag of Lime chips are $0.40, and for a bag of
   Vinegar chips $0.50. Which of the following is not a feasible production
   combination?
19. The linear programming model for a transportation problem has
   constraints for supply at each source and demand at each destination.

20. For a maximization problem, assume that a constraint is binding. If the
   original amount of a resource is 4 lbs., and the range of feasibility
   (sensitivity range) for this constraint is from
   3 lbs. to 6 lbs., increasing the amount of this resource by 1 lb. will result in
   the
21. In a total integer model, all decision variables have integer solution
   values.
22. Linear programming is a model consisting of linear relationships
   representing a firm's decisions given an objective and resource
   constraints.
23. When using linear programming model to solve the "diet" problem, the
   objective is generally to maximize profit.
24. In a balanced transportation model where supply equals demand, all
   constraints are equalities.
25. In a transportation problem, items are allocated from sources to
   destinations at a minimum cost.
26. Mallory Furniture buys 2 products for resale: big shelves (B) and medium
   shelves (M). Each big shelf costs $500 and requires 100 cubic feet of
   storage space, and each medium shelf costs $300 and requires 90 cubic
   feet of storage space. The company has $75000 to invest in shelves this
   week, and the warehouse has 18000 cubic feet available for storage.
   Profit for each big shelf is $300 and for each medium shelf is $150. Which
   of the following is not a feasible purchase combination?
27. In a mixed integer model, some solution values for decision variables are
   integer and others can be non-integer.
28. In a 0 - 1 integer model, the solution values of the decision variables are 0
   or 1.
29. Determining the production quantities of different products manufactured
   by a company based on resource constraints is a product mix linear
   programming problem.
  30. Determining the production quantities of different products manufactured
     by a company based on resource constraints is a product mix linear
     programming problem.
  31. When the right-hand sides of 2 constraints are both increased by 1 unit,
     the value of the objective function will be adjusted by the sum of the
     constraints' prices.
  32. The transportation method assumes that
  33. A constraint is a linear relationship representing a restriction on decision
     making.
  34. When formulating a linear programming model on a spreadsheet, the
     measure of performance is located in the target cell.
  35. The linear programming model for a transportation problem has
     constraints for supply at each ________ and _________ at each
     destination.
  36. The 3 types of integer programming models are total, 0 - 1, and mixed.
  37. In using rounding of a linear programming model to obtain an integer
     solution, the solution is

  38. If we use Excel to solve a linear programming problem instead of QM for
     Windows,
     then the data input requirements are likely to be much less tedious and
     time consuming.
  39. In a _______ integer model, some solution values for decision variables
     are integer and others can be non-integer.
  40. Which of the following is not an integer linear programming problem?

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Description: Assignments: Week 3 Assignment 1: JET Copies Case Problem Read the “JET Copies” Case Problem on pages 678-679 of the text. Using simulation estimate the loss of revenue due to copier breakdown for one year, as follows: 1. In Excel, use a suitable method for generating the number of days needed to repair the copier, when it is out of service, according to the discrete distribution shown. 2. In Excel, use a suitable method for simulating the interval between successive breakdowns, according to the continuous distribution shown. 3. In Excel, use a suitable method for simulating the lost revenue for each day the copier is out of service. 4. Put all of this together to simulate the lost revenue due to copier breakdowns over 1 year to answer the question asked in the case study. 5. In a word processing program, write a brief description/explanation of how you implemented each component of the model. Write 1-2 paragraphs for each component of the model (days-to-repair; interval between breakdowns; lost revenue; putting it together). 6. Answer the question posed in the case study. How confident are you that this answer is a good one? What are the limits of the study? Write at least one paragraph. Week 4 Assignment 2: Internet Field Trip - Forecasting Methods 1. Research: Research at least six (6) information sources on forecasting methods; take notes and record and interpret significant facts, meaningful graphics, accurate sounds and evaluated alternative points of view. 2. Preparation: Produce as storyboard with thumbnails of at least ten (10) slides. Include the following elements: Title of slide, text, background color, placement & size of graphic, fonts - color, size, type for text and headings Hyperlinks (list URLs of any site linked from the slide), narration text, and audio files (if any) o Number on slides clear o Logical sequence to the presentation 3. Content: Provide written content with the following elements: o introduction tha