Susan Shouter, the advertising manager for Productions Inc., is considering two

Question

Susan Shouter, the advertising manager for Productions Inc., is considering two possible advertising media to promote a new product line. Television ads cost $900 each, while radio ads cost $600 each. The total budget is $10,500 per week. There must be at least 2 ads of each type, and there should be no more than 19 ads in total. The company wants the number of tv ads to be no more than twice the number of radio ads.

Each television ad reaches 60,000 people; while each radio ad reaches 20,000 people. The company wishes to reach as many respondents as possible while meeting all the constraints stated.

Write the appropriate LP model for determining the number of ads of each type that should be placed.

Explanation / Answer

Let number of tv ads per week be x and radio ads per week be y

The cost will be 900*x+600*y

Given budget is 10500

Hence, 900*x+600*y<=10500

As there must be at least 2 ads of each type

so, x>=2 and y>=2

or, -x<=-2 and -y<=-2

Number of total ads=x+y

Total ads should not be more than 19

hence, x+y<=19

Number of tv ads should be not more than twice the radio ads

x<=2*y

Total reach=60000*x+20000*y

We have to maximize the total reach

Maximize 60000*x+20000*y

s.t.

900*x+600*y<=10500

-x<=-2

-y<=-2

x+y<=19

x<=2*y

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