Question

Solve the problem.

Formulate the following problem as a linear programming problem (DO NOT SOLVE):A shoe company is introducing a new line of running shoes. The marketing division decides to promote the line in a particular city. The promotion will consist of newspaper, radio, and television ads. Each newspaper ad will cost $120, each television ad will cost $370, and each radio ad will cost $210. The company wants to spend at most half their money on newspaper ads. The marketing division believes that each newspaper ad will reach 4,700 men and 3,700 women, each television ad will reach 7,600 men and 6,600 women, and each radio ad will reach 4,500 men and 5,500 women. The promotion will be considered successful if it reaches at least 400,000 men and 200,000 women. How should the company divide its money between the newspaper, television, and radio ads so as to insure a successful promotion at a minimum cost? (Let x ₁ equal the number of newspaper ads, x ₂ equal the number of television ads, and x ₃ equal the number of radio ads purchased in the promotion.)

A

Minimize

C = -120x1 - 370x2 + 210x3

subject to

B

Minimize

C = 120x1 + 370x2 + 210x3

subject to

C

Minimize

C = -120x1 - 370x2 + 210x3

subject to

D

Maximize

C = 120x1 + 370x2 + 210x3

subject to

Answer 1