Question

Question #2 A candidate for mayor in a small town has allocated $50,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $250 and reaches an estimated 4,000 people. Each television ad costs $550 and reaches an estimated 8,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 9 radio adds and at least 10 TV ads be produced. How many ads of each type should be used? How many people will this reach?

Answer 1

Let x1 and x2 represent the number of radio and television ads

=>

Maximize people reached = 4000x1 + 8000x2

subject to

250x1 + 550x2 <= 50000

x1 >= 9

x2 >=10

Solving graphically

Hence the critical points are (9,10) , (178,10), (9,86.82)

Z(9,10) = 4000 * (9) + 8000(10) = 116000

Z(178,10) = 4000 * 178 + 8000 * 10 = 792000

z(9,86) = 4000 *9 + 8000 * 86 = 724000

Hence choose (178,10)

so,

No of radio ads = 178

No of tv ads = 10

Total reach = 792000