Marketing and Finance Applications by 5R42zo5

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									Readings



                           Readings
   Chapter 4
   Linear Programming Applications in Marketing, Finance,
   and Operations Management




           BA 452 Lesson I.8 Marketing and Finance Applications   1
Overview



                           Overview




           BA 452 Lesson I.8 Marketing and Finance Applications   2
Overview

   Media Selection Problems help marketing managers allocate a fixed advertising
   budget to various advertising media. The objective is to maximize reach,
   frequency, and quality of exposure.

   Marketing Research Problems help marketing managers learn about consumer
   characteristics and preferences, by surveying sufficiently many people at
   minimum cost.

   Portfolio Selection Problems with Dynamic Constraints help select specific
   investments (stocks, bonds, …) over time to either maximize expected return or
   minimize risk.

   Financial Planning Problems help financial managers meet future budget
   obligations by selecting specific investments (stocks, bonds, …) over time to
   produce future income at minimum cost.




                 BA 452 Lesson I.8 Marketing and Finance Applications               3
Overview


   Tool Summary
      One possible way to solve a program where some variables are
       restricted to be integers (like the number of ads in Example 1): Do
       not restrict the variables to be integers, and maybe the variables at
       an optimum will be integers.
        • Warning: This does not always work: without integer restrictions,
           some variables at an optimum may not be integers --- even if all
           coefficients in the linear program are integers (like in an Example
           in Lesson I-3).
      Use compound variables:
        • First Example: EFR = number of evening ads on Friday
        • Second Example: Gi = amount of new investment in
           government bonds in month i
        • Third Example: SO1 = number of standard wheels made with
           overtime labor in month 1


               BA 452 Lesson I.8 Marketing and Finance Applications              4
Tool Summary


   Tool Summary
      Use dynamic or recursive constraints:
        • Second Example: Constrain that Month 2's total investment be
          limited to principle and interest invested locally in Month 1:
          G2 + C2 + L2 = 1.0075L1
      Use inventory variables:
        • Second Example: SI = number of standard wheels held in
          inventory from month 1 to month 2




               BA 452 Lesson I.8 Marketing and Finance Applications        5
Media Selection



                       Media Selection




              BA 452 Lesson I.8 Marketing and Finance Applications   6
Media Selection


   Overview

   Media Selection Problems help marketing managers
   allocate a fixed advertising budget to various advertising
   media. Potential media include newspapers, magazines,
   radio, television, and direct mail. The objective is to
   maximize reach, frequency, and quality of exposure.
   Constraints may restrict permissible allocations by
   company policy, contract requirements, and media
   availability.




              BA 452 Lesson I.8 Marketing and Finance Applications   7
Media Selection


   Question: SMM Company recently developed a new instant
   salad machine, and has $282,000 to spend on advertising.
   The product is to be initially test marketed in the Dallas
   area. The money is to be spent on a TV advertising blitz
   during one weekend (Friday, Saturday, and Sunday) in
   November.

   The three options available are: daytime advertising,
   evening news advertising, and Sunday game-time
   advertising. A mixture of one-minute TV spots is desired.




              BA 452 Lesson I.8 Marketing and Finance Applications   8
Media Selection



                             Estimated Audience
      Ad Type               Reached With Each Ad             Cost Per
      Ad
      Daytime                         3,000                       $5,000
      Evening News                     4,000                      $7,000
      Sunday Game                     75,000                    $100,000

      SMM wants to take out at least one ad of each type
      (daytime, evening-news, and game-time). Further, there
      are only two game-time ad spots available. There are
      ten daytime spots and six evening news spots available
      daily. SMM wants to have at least 5 ads per day, but
      spend no more than $50,000 on Friday and no more
      than $75,000 on Saturday.

              BA 452 Lesson I.8 Marketing and Finance Applications         9
Media Selection



      What should be SMM’s objective?
      Are you making any implicit assumptions?




              BA 452 Lesson I.8 Marketing and Finance Applications   10
Media Selection




              BA 452 Lesson I.8 Marketing and Finance Applications   11
Media Selection
   Define the decision variables
    DFR = number of daytime ads on Friday
    DSA = number of daytime ads on Saturday
    DSU = number of daytime ads on Sunday
    EFR = number of evening ads on Friday
    ESA = number of evening ads on Saturday
    ESU = number of evening ads on Sunday
    GSU = number of game-time ads on Sunday
  Define the objective function
    Maximize the total audience reached
  = Max (audience per ad of each type)x(number of ads used of each type)
    Max 3000DFR +3000DSA +3000DSU +4000EFR
        +4000ESA +4000ESU +75000GSU




              BA 452 Lesson I.8 Marketing and Finance Applications         12
Media Selection

    Define the constraints to take out at least one ad of each type:
      (1) DFR + DSA + DSU > 1
      (2) EFR + ESA + ESU > 1
      (3) GSU > 1
    Define the constraints of ten daytime spots available:
      (4) DFR < 10; (5) DSA < 10;           (6) DSU < 10
    Define the constraints of six evening news spots available:
      (7) EFR < 6;      (8) ESA < 6;         (9) ESU < 6




               BA 452 Lesson I.8 Marketing and Finance Applications     13
Media Selection
    Define the constraint of only two Sunday game-time ad spots available:
     (10) GSU < 2
    Define the constraint of at least 5 ads per day:
      (11) DFR + EFR > 5; (12) DSA + ESA > 5;
      (13) DSU + ESU + GSU > 5
    Define the constraint of spending no more than $50,000 on Friday:
      (14) 5000DFR + 7000EFR < 50000
    Define the constraint of spending no more than $75,000 on Saturday:
      (15) 5000DSA + 7000ESA < 75000
    Define the constraint of spending no more than $282,000 in total:
      (16) 5000DFR + 5000DSA + 5000DSU + 7000EFR
                      + 7000ESA + 7000ESU + 100000GSU7 < 282000




              BA 452 Lesson I.8 Marketing and Finance Applications            14
Media Selection




                  Interpretation: Total new audience reached = 199,000
                  Number of daytime ads on Friday      = 8
                  Number of daytime ads on Saturday = 5
                  Number of daytime ads on Sunday = 2
                  Number of evening ads on Friday      = 0
                  Number of evening ads on Saturday = 0
                  Number of evening ads on Sunday             = 1
                  Number of game-time ads on Sunday = 2

              BA 452 Lesson I.8 Marketing and Finance Applications       15
Marketing Research



                 Marketing Research




             BA 452 Lesson I.8 Marketing and Finance Applications   16
Marketing Research


   Overview

   Marketing Research Problems help marketing managers
   learn about consumer characteristics and preferences.
   Marketing research firms design and solve such problems
   to survey sufficiently many people at minimum cost.




             BA 452 Lesson I.8 Marketing and Finance Applications   17
Marketing Research


   Question: C R Market Surveys, Inc. specializes in
   evaluating consumer reaction to new products and
   advertising campaigns. A client hired Market Survey Inc. to
   measure consumer reaction to a recently marketed
   product. Market Survey Inc. agreed to conduct interviews
   from households, both with or without children, during
   either the day or evening.




             BA 452 Lesson I.8 Marketing and Finance Applications   18
Marketing Research


   The client’s contract calls for 1000 interviews under the following
   quotas:
   1. Interview at least 400 households with children.
   2. Interview at least 400 households without children.
   3. Interview at least as many households at night, as during the day.
   4. Of the interviews of households with children, at least 40 percent
      must be during the evening.
   5. Of the interviews of households without children, at least 60
      percent must be during the evening.
   Based on previous studies, here are the estimated interview costs:
                Household             Day             Evening
                 Children             $20                $25
               No Children             $18               $20
   Formulate the Marketing Research Problem for finding the minimum-
   cost household, time-of-day interview plan satisfying all quotas.

             BA 452 Lesson I.8 Marketing and Finance Applications          19
Marketing Research


   Answer: Define decision variables
   DC = the number of daytime interviews of households with
   children
   DN = the number of daytime interviews of households with
   no children
   EC = the number of evening interviews of households with
   children
   EN = the number of evening interviews of households with
   no children




             BA 452 Lesson I.8 Marketing and Finance Applications   20
Marketing Research



               Household              Day             Evening
                Children              $20                $25
               No Children            $18                $20


   Given cost per unit, minimize total cost:
   Min 20DC + 18DN + 25EC + 20EN




             BA 452 Lesson I.8 Marketing and Finance Applications   21
Marketing Research


   Formulate Constraints:
   1. Interview at least 1000 households:
   DC + DN + EC + EN > 1000
   2. Interview at least 400 households with children:
   DC + EC > 400
   3. Interview at least 400 households without children:
   DN + EN > 400
   4. Interview at least as many households at night, as during the day:
   EC + EN > DC + DN
   5. Of the interviews of households with children, at least 40 percent
      must be during the evening:
   EC > 0.40(DC + EC)
   6. Of the interviews of households without children, at least 60
      percent must be during the evening:
   EN > 0.60(DN + EN)

             BA 452 Lesson I.8 Marketing and Finance Applications          22
Portfolio Selection with Dynamic Constraints



       Portfolio Selection with Dynamic
                  Constraints




              BA 452 Lesson I.8 Marketing and Finance Applications   23
Portfolio Selection with Dynamic Constraints


    Overview

    Portfolio Selection Problems with Dynamic Constraints help
    financial managers select specific investments (stocks,
    bonds, …) over time to either maximize expected return or
    minimize risk. Dynamic Constraints may restrict new
    investment in one period to equal the return from
    investments in previous periods. For example, there may
    be no new investments one month if all investments in
    previous months have not yet matured.




              BA 452 Lesson I.8 Marketing and Finance Applications   24
Portfolio Selection with Dynamic Constraints


      Question: Pepperdine University has $20 million available for
      investment. It wishes to invest over the next four months in
      such a way that it will maximize the total interest earned (after
      all investments mature) as well as have at least $10 million
      available at the start of the fifth month for a high rise building
      venture in which it will be participating. For the time being,
      Pepperdine wishes to invest only in 2-month government
      bonds (earning 2% over the 2-month period) and 3-month
      construction loans (earning 6% over the 3-month period).
      Each of these is available each month for investment. Funds
      not invested in these two investments are liquid and earn 3/4
      of 1% per month when invested locally.

      How should Pepperdine invest over the next four months if at no
      time does it wish to have more than $8 million in either government
      bonds or construction loans?

              BA 452 Lesson I.8 Marketing and Finance Applications          25
Portfolio Selection with Dynamic Constraints


    Answer: Define the decision variables
      Gi = amount of new investment in government
            bonds in month i (for i = 1, 2, 3, 4)
      Ci = amount of new investment in construction
            loans in month i (for i = 1, 2, 3, 4)
      Li = amount invested locally in month i (for i = 1, 2, 3, 4)




               BA 452 Lesson I.8 Marketing and Finance Applications   26
Portfolio Selection with Dynamic Constraints


       Define the objective function
        Maximize total interest earned after all investments mature:
        Max (interest rate on investment) X (amount invested)
        Max .02G1 + .02G2 + .02G3 + .02G4
              + .06C1 + .06C2 + .06C3 + .06C4
              + .0075L1 + .0075L2 + .0075L3 + .0075L4




                BA 452 Lesson I.8 Marketing and Finance Applications   27
Portfolio Selection with Dynamic Constraints
 Constrain that Month 1's total investment be $20 million:
         (1) G1 + C1 + L1 = 20,000,000
 Constrain that Month 2's total investment be limited to principle and interest
  invested locally in Month 1:
         (2) G2 + C2 + L2 = 1.0075L1 , or G2 + C2 - 1.0075L1 + L2 = 0
 Constrain that Month 3's total investment be limited to principle and interest
  invested in government bonds in Month 1 and locally invested in Month 2:
         (3) G3 + C3 + L3 = 1.02G1 + 1.0075L2 , or - 1.02G1 + G3 + C3 -
  1.0075L2 + L3 = 0




               BA 452 Lesson I.8 Marketing and Finance Applications           28
Portfolio Selection with Dynamic Constraints


   Constrain that Month 4's total investment be limited to principle and interest
    invested in construction loans in Month 1, government bonds in Month 2,
    and locally invested in Month 3:
    (4) G4 + C4 + L4 = 1.06C1 + 1.02G2 + 1.0075L3 , or
           - 1.02G2 + G4 - 1.06C1 + C4 - 1.0075L3 + L4 = 0
   Constrain that $10 million must be available at start of Month 5:
    (5) 1.02G3 + 1.06C2 + 1.0075L4 > 10,000,000




                BA 452 Lesson I.8 Marketing and Finance Applications             29
Portfolio Selection with Dynamic Constraints
   Constrain that no more than $8 million be in government bonds at any time:
    (6) G1       < 8,000,000;       (7) G1 + G2 < 8,000,000
    (8) G2 + G3 < 8,000,000;        (9) G3 + G4 < 8,000,000
   Constrain that no more than $8 million be in construction loans at any time:
    (10) C1             < 8,000,000; (11) C1 + C2           < 8,000,000
    (12) C1 + C2 + C3 < 8,000,000; (13) C2 + C3 + C4 < 8,000,000




                 BA 452 Lesson I.8 Marketing and Finance Applications              30
Portfolio Selection with Dynamic Constraints




    Interpretation: Total interest earned in the 4-month
    period = $1,429,213.80.
    Gi = invested in government bonds
    Ci = invested in construction loans
    Li = invested locally, in month i (for i = 1, 2, 3, 4)
              BA 452 Lesson I.8 Marketing and Finance Applications   31
Financial Planning



                     Financial Planning




              BA 452 Lesson I.8 Marketing and Finance Applications   32
Financial Planning


   Overview

   Financial Planning Problems help financial managers meet
   future budget obligations by selecting specific investments
   (stocks, bonds, …) over time to produce future income.
   The goal is to meet those obligations at minimum cost.




              BA 452 Lesson I.8 Marketing and Finance Applications   33
Financial Planning


   Question: Hewlitt Corporation established an early
   retirement program as part of its corporate restructuring.
   68 employees selected early retirement. The company
   thus incurs the following obligations over the next eight
   years:

        Year     1         2         3         4         5         6         7         8
        Cash   430,000   210,000   222,000   231,000   240,000   195,000   225,000   255,000
        Req.

   The requirements are due at the beginning of each year.

   The corporate treasurer must determine how much money
   must be set aside today to meet the eight yearly obligations
   as they come due.

               BA 452 Lesson I.8 Marketing and Finance Applications                            34
Financial Planning


   The financial plan for the retirement program includes
   savings, and government bonds. There are three bond
   choices available at the beginning of year 1:
                             Market                      Years to
                Bond                      Rate (%)
                             Price                       Maturity
                     1       $1,150         8.875           5
                     2       $1,000         5.500           6
                     3       $1,350        11.750           7

   The government bonds have a par value of $1000, which
   means that even with different prices, each bond pays
   $1000 at maturity. The rates shown are based on the par
   value. (For example, each unit of Bond 1 pays $88.75
   each year for 5 years.) Each year, all money not invested
   in bonds earns an annual rate of 4%.
              BA 452 Lesson I.8 Marketing and Finance Applications   35
Financial Planning


   Answer:
   Define decision variables
   F = total dollars required to meet the retirement plan’s eight
   year obligation
   B1 = units of bond 1 purchased at the beginning of year 1
   B2 = units of bond 2 purchased at the beginning of year 1
   B3 = units of bond 3 purchased at the beginning of year 1
   Si = dollars in savings at the beginning of year i, (i = 1,…,8)




              BA 452 Lesson I.8 Marketing and Finance Applications   36
Financial Planning


   Define objective
   Minimize F

   Define Constraints
   For each of the eight years,
   (Funds available at the beginning of the year)
   - (Funds invested in bonds and placed in savings)
   = (Cash obligation for the current year)




              BA 452 Lesson I.8 Marketing and Finance Applications   37
Financial Planning


   For year 1,
   (Funds available at the beginning of the year) = F,
   (Funds invested in bonds and placed in savings) =
   1150B1 + 1000B2 + 1350B3 + S1,
   (Cash obligation for the current year) = 430000,
   so the constraint reads
   F - 1150B1 - 1000B2 - 1350B3 - S1 = 430000




              BA 452 Lesson I.8 Marketing and Finance Applications   38
Financial Planning


   For year 2,
   (Funds available at the beginning of the year) =
   88.75B1 + 55B2 + 117.5B3 + 1.04S1,
   (Funds placed in savings) = S1,
   (Cash obligation for the current year) = 210000,
   so the constraint reads
   88.75B1 + 55B2 + 117.5B3 + 1.04S1 – S2 = 210000




              BA 452 Lesson I.8 Marketing and Finance Applications   39
Financial Planning


   For year 3,
   88.75B1 + 55B2 + 117.5B3 + 1.04S2 – S3 = 222000
   For year 4,
   88.75B1 + 55B2 + 117.5B3 + 1.04S3 – S4 = 231000
   For year 5,
   88.75B1 + 55B2 + 117.5B3 + 1.04S4 – S5 = 240000
   For year 6, since Bond 1 matures,
   1088.75B1 + 55B2 + 117.5B3 + 1.04S5 – S6 = 195000
   For year 7, since Bond 2 matures,
   1055B2 + 117.5B3 + 1.04S6 – S7 = 225000
   For year 8, since Bond 3 matures,
   1117.5B3 + 1.04S6 – S7 = 225000

              BA 452 Lesson I.8 Marketing and Finance Applications   40
Financial Planning


   Management Scientist reveals the optimal solution to this
   12-variable, 8-constraint problem,
   B1 = 144.988, B2 = 187.856, B3 = 228.188
   so
   $1150(144.988) = $166,736 is invested in Bond 1,
   $1150(187.856) = $187,856 is invested in Bond 2,
   $1150(228.188) = $308,054 is invested in Bond 3.

   F = 1728793.85, so $1,728,793.85 is the minimum starting
   investment for the company can make the specified
   investments and generate future income to meet its budget
   obligations.


              BA 452 Lesson I.8 Marketing and Finance Applications   41
BA 452                                                Quantitative Analysis



                End of Lesson I.8




         BA 452 Lesson I.8 Marketing and Finance Applications            42

								
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