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Operations Research Operations Research From the material in

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					Operations Research

From the material in Chapter 8, solve the following three problems: (60 points)

For each of the assigned problems, you must submit the following:

      Problem Formulation
     (including a descriptive listing of all variables used and the formulation in non-standard form,
     that is, with inequalities)

     Solution output

     Answers to all component questions with references to the solution where appropriate.


      Remember, you MUST clearly define your variables, show your objective function and all
     constraints in non-standard form.

     Make sure that all appropriate values are shown.


Problem #1 Stoller Manufacturing Company
Stoller Manufacturing Company produces fuel injection assembly units for automobile and light
truck manufacturers at its facility in Evanston, Arkansas. The company has experienced rapid
growth in recent years and is planning to build at least one new plant. Three cities are currently
being considered: Baytown, Texas; Lake Charles, Louisiana; and Mobile, Alabama. Once the
plant or plants are completed and on line, Stoller Manufacturing wants to have sufficient new
capacity to produce at least 38,000 units each year. The Baytown facility would have an annual
fixed cost of $340,000 and a production capacity maximum of 21,000 units. The annual fixed
cost for the Lake Charles facility would be $270,000 with a maximum production capacity of
20,000 units. The Mobile facility would be able to produce a maximum of 19,000 units and the
annual fixed cost would be $290,000. The variable cost per unit at each of the facilities is
projected to be $32, $33, and $30 at the Baytown, Lake Charles, and Mobile locations
respectively.
a. Formulate an appropriate linear programming model that can be used to determine the optimal
number and location of any new facility or facilities to complement the production capacity for
Stoller Manufacturing.
b. Determine the optimal new production capacity plan for Stoller Manufacturing, using the
Management Scientist software, including the number of new facilities represented, the new
production capacity added, if any, and the total cost of any additional capacity. Provide a
narrative that explains the Management Scientist solution used.
Problem #2 San Francisco Metropolitan Arts Council
The Metropolitan Arts Council of San Francisco is planning an advertising campaign to promote
its upcoming season of plays, concerts, and ballet performances. Several media opportunities
are under consideration. A local television commercial announcement costing $25,000 is
expected to reach an estimated 53,000 potential arts customers consisting of 12,000 males and
20,000 females over the age of 35 and 7,000 males and 14,000 females under the age of 35. A
newspaper ad costs $7,000 and is expected to reach 30,000 potential arts customers consisting
of 12,000 males and 8,000 females over the age of 35 and 6,000 males and 4,000 females under
the age of 35. Lastly, a local radio program ad costing $9,000 is expected to reach an audience
of 41,000 potential arts customers consisting of 7,000 males and 11,000 females over 35 and
10,000 males and 13,000 females who are under 35 years of age.
The arts council has established several guidelines in its promotional strategy. The council wants
to reach at least 200,000 potential arts customers at the least cost. The council believes people
over the age of 35 are more likely to purchase tickets to these events and wants to reach at least
one and a half times as many potential customers who are over 35 as those who are under that
age. The council also believes that women are more likely to initiate ticket purchases to the arts
than men and therefore wants its overall audience to be at least 60% female.
a. Formulate a linear programming model that can be used to determine the optimal media
selection strategy that yields the minimum cost solution for the San Francisco Metropolitan Arts
Council.
b. Determine the optimal media selection strategy using the Management Scientist software,
including the quantity of each media type selected and the total cost. Provide a narrative that
explains the Management Scientist solution used.
Problem #3 Pearson Mortgage Associates
Pearson Mortgage Associates is a large home mortgage servicing firm located in the Northeast.
Pearson has a pool of permanent and temporary staff that process mortgage account payments
and update escrow accounts for insurance and taxes. A permanent staff associate can process
220 accounts per day with an average of 0.4 errors and is paid $900.00 for a standard 40 hour
workweek. A temporary staff associate, an employee with less than two years experience, can
process 140 accounts per day with an average of 0.9 errors and is paid $112.50 for a standard 8
hour workday. Pearson has 32 workstations available for associates and must process at least
6,300 accounts daily. The company wants to limit total errors, which must be researched and
resolved by managers, to a maximum of 15 per day. Pearson Mortgage Associates is
considering retaining some hourly part-time associates to support the permanent and temporary
staff associates positions. Part-time associates are assumed to be able to process 12 accounts
per hour with an average of 0.16 errors and would be paid $8.75 per hour.
a. Formulate an appropriate linear programming model that can be used to determine the optimal
staffing plan for Pearson Mortgage Associates.
b. Determine the optimal staffing plan using the Management Scientist software, including the
number of employees in each associate category and the total cost. Determine the hourly rate
for part-time associates that would preclude consideration of this category to replace temporary
staff associates. Provide a narrative that explains the Management Scientist solution used.

Business Statistics

From the material in Chapter 8 of the Business Statistics text, solve the following three problems:
(40 points)

You must show all of your work (formulas used, intermediate steps, etc.). Correct answers
without backup will not be given credit.

Problem #4 The National Quality Research Center
The National Quality Research Center at the University of Michigan provides a quarterly measure
of consumer opinions about products and services (The Wall Street Journal, February 18, 2003).
A survey of 10 restaurants in the Fast Food/ Pizza group showed a sample mean customer
satisfaction index of 71. Past data indicate that the population standard deviation of the index has
been relatively stable with σ=5.
a. Explain what assumption the researcher should be willing to make if a margin of error is
desired.
b. Using 95% confidence, determine the margin of error.
c. Determine the margin of error if 99% confidence is desired.

Problem #5 PC Magazine survey
In a recent survey of 1677 U.S. Internet users, 74% of the young tech elite (average age
of 22) say their computer would be very hard to give up (PC Magazine, February 3,
2004). Only 48% say their television would be very hard to give up.
a. Develop a 95% confidence interval for the proportion of the young tech elite that
would find it very hard to give up their computer.
b. Develop a 99% confidence interval for the proportion of the young tech elite that
would find it very hard to give up their television.
c. Determine in which case, part (a) or part (b), the margin of error is larger. Explain
why.
Problem #6 News Information survey
In a survey, 200 people were asked to identify their major source of news information; 110 stated
that their major source was television news.
a. Construct a 95% confidence interval for the proportion of people in the population who consider
television their major source of news information.
b. Determine how large a sample would be necessary to estimate the population proportion with
a margin of error of .05 at 95% confidence.

				
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