5. Pormulate only the tollowing goa! problem. DEFIN tirst! There E your variable

Question

5. Pormulate only the tollowing goa! problem. DEFIN tirst! There E your variables aredecision variables in this problem An advertising company wishes to plan an advertising canpaign in thee different media-television, radio, and nagazines. The purpose of the advertising program is to reach as many of the potential customers as possible. Results of a market study are given below: Radio Magazines Television Daytine Prime Time Cost of an advertising unit $40,000 $65,000 $30,000 $15,000 Number of potential customers reached per unit 400,000 900,000 500,000 300,000 Number of wonen customers reached per unit 700,000 400,000 500,000 100,000 The company has an advertising budget of $700,000 and has the following goals to achieve in order of importance: 1. At least 3 million exposures should take place among women. 2. Advertising on television to be limited to $500,000. 3. Achieve total exposure of 4 million potential customer. 4. Advertising budget should not be exceeded by more than 108. 5. The number of advertising units on radio and nagazine should each be between 5 and 10. 6. At least 3 advertising units to be bought on daytime television, and 2 units during prime time

Explanation / Answer

There are _ 20 _ decision variables. 4 of them are standard variables and 16 deviation variables.

Standard variables:

X1 = Units of daytime TV Ads to purchase

X2 = Units of Primetime TV Ads to purchase

X3 = Units of Radio Ads to purchase

X4 = Units of Magazine Ads to purchase

Objective: Min 6d1- + 5*(30/5)*d2+ + 4*(3/4)d3- + 3*(30/7.7)*d4+ + 2*(3*10^6/5)*d5- + 2*(3*10^6/10)*d6+  + 2*(3*10^6/5)*d7- + 2*(3*10^6/10)*d8+ + (3*10^6/3)*d9- + (3*10^6/2)d10-    

Goal constraints:

700000X1 + 400000X2 + 500000X3 + 100000X4 - d1+ + d1- = 3000000

40000X1 + 65000X2 - d2+ + d2- = 500000

400000X1 + 900000X2 + 500000X3 + 300000X4 - d3+ + d3- = 4000000

40000X1 + 65000X2 + 30000X3 + 15000X4 - d4+ + d4- = 770000

X3  - d5+ + d5- = 5

X3 - d6+ + d6- = 10

X4 - d7+ + d7- = 5

X4 - d8+ + d8- = 10

X1 - d9+ + d9- = 3

X2 - d10+ + d10- = 2

X1, X2, X3, X4, d1+, d1-, d2+, d2-, d3+, d3-, d4+, d4-, d5+, d5-, d6+, d6-, d7+, d7-, d8+, d8-, d9+, d9-, d10+, d10- >= 0

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