BUAD306 - Assignment 4 - Graded A+ solution

Assignment 4

Goal Programming

1.      The Relax-and-Enjoy Lake Development Corporation is developing a lakeside community at a privately owned lake and is in the business of selling property for vacation and/or retreat cottages.  The primary market for these lakeside lots includes all middle and upper income families within approximately 100 miles of the development.  Relax-and-Enjoy has employed the advertising firm of Boone, Phillips and Jackson to design the promotional campaign for the project.

           After considering possible advertising media and the market to be covered, 

     Boone has made the preliminary recommendation to restrict the first month’s

     advertising to five sources.  At the end of this month, Boone will then reevaluate

     its strategy based upon the month’s results.  Boone has collected data on a number

     of potential purchase families reached, the cost per advertisement, the maximum

     number of times each medium is available, the expected exposure for each of the

     five media.  The expected exposure is measured in terms of an exposure unit, a

     management judgment measure of the relative value of one advertisement in each

     of the media.  The measures based on Boone’s experience in the advertising

     business take into account such factors as audience profile (age, income, and

     education of the audience reached), image presented, and quality of the

     advertisement.  The information collected to date is presented below.

                                          Advertising Media Alternatives for the

                              Relax-and-Enjoy Lake Development Corporation

                                  Number of                 

                                  Potential                           Maximum

                                  Purchase     Cost per            Times                Expected

                                  Families      Advertise-      Available             Exposure

    Advertising Media      Reached      ment               per Month*          Units

1.  Daytime TV (1 min)    1000          $1500                 15                       65

     Station WKLA

2.  Evening TV (30s)        2000          $3000                 10                       90

     Station WKLA

3.  Daily newspaper          1500            $400                 25                       40

     (full page), The

     Morning Journal

4.  Sunday newspaper       2500           $1000                  4                       60

     Magazine (1/2 pg.

     Color).  The Sunday

     Press.

5.  Radio, 8:00 a.m. or        300              $100               30                       20

     5:00 p.m. news (30’s)

 __Station KNOP_________________________________________________________

*The maximum number of times the medium is available is either the maximum number of times the advertising medium occurs (e.g. four Sundays for medium 4) or the maximum number of times Boone will allow the medium to be used. 

     Relax-and-Enjoy has provided Boone with an advertising budget of $30,000 for the first month’s campaign.  In addition Relax-and-Enjoy has the following goals and priorities regarding how Boone allocates these funds, as follows:

            Goal 1:   To utilize at least 10 television commercials (Priority 1).

            Goal 2:   To reach at least 50,000 potential purchases during the month 

                           (Priority 2).

            Goal 3:   To spend no more than $18,000 on television advertisements

                           (Priority 3).

            Goal 4:   To come as close as possible to achieving 2400 exposure units

                           (Priority 4).

            Goal 5:   To minimize the advertising budget (Priority 5).

(a)    Formulate a goal programming model of this problem:

Economic constraints:

Goal constraints:

Objective function:

(b)   Suppose that Boone is working on a similar but smaller problem for

      another client, and they are considering only two media alternatives,

      evening T.V. and the daily newspaper.  This second problem can be

      modified as follows:

3000 X1 + 400 X2 = $24,000 Budget

X1  -  d1⁺ + d1^- = 7

X2 – d2⁺ + d2^- = 15

2000 X1 + 1500 X2 – d3⁺ + d3^- = 30,000

Min Z= P1 d1^-   + P2  d2⁺ + P3 d3^- + P4  (-d1⁺)

Determine the optimal solution for this problem.  Give the values of all variables.