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• Due on 03 Feb, 2015 11:13:00
• Asked On 31 Jan, 2015 11:44:49
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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.

Relax-and-Enjoy Lake Development Corporation

Number of

Potential                           Maximum

Purchase     Cost per            Times                Expected

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).

(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:

DTV= Daytime TV, ETV= Evening TV, DNP= Daily Newspaper, SNP= Sunday Newspaper, R= Radio

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.

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GOAL PROGRAMMING *** (A+) ***
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• Submitted On 02 Feb, 2015 09:41:09
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