Question

Acme Advertising has a $10,000 budget for a combination of television ads ($300 each) and radio ads ($125 each) for a new client (a sporting goods store) and wants to maximize total reach. Television ads reach 5,000 people while radio ads reach 3,500 people.
The television ads are to be run during local college basketball games with the goal of running at least 5 ads and no more than 20 ads. Radio ads will be run at the same time during the game and the goal is to run at least radio 10 ads.

a)Formulate with linear programming to maximize reach.

b)Determine the optimal solution.

c) Due to high television ratings, TV reach has increased from 5,000 viewers to 8,500 viewers. How would this change the optimal solution?

d)If the manager decides the minimum TV ads should be 10 instead of 5, how does this change the optimal solution?

Answer 1

a)

Number of Television Ads = X1

Number of Radio Ads=X2

Objective function, Maximizing total reach= 5000*X1+3500*X2

Subject to:

300*X1+125*X2=<10000

X1>=5

X1=<20

X2>=10

X1 and X2>=0

b)

Number of Television Ads = X1=5

Number of Radio Ads=X2=68

Maximized total reach=263000

c)

Objective function, Maximizing total reach= 8500*X1+3500*X2

Subject to:

300*X1+125*X2=<10000

X1>=5

X1=<20

X2>=10

X1 and X2>=0

Number of Television Ads = X1=20

Number of Radio Ads=X2=32

Maximized total reach=282000

d)

Objective function, Maximizing total reach= 5000*X1+3500*X2

Subject to:

300*X1+125*X2=<10000

X1>=10

X1=<20

X2>=10

X1 and X2>=0

Number of Television Ads = X1=10

Number of Radio Ads=X2=56

Maximized total reach=246000