Question

A company is planning how to use its $225,000 advertising budget to increase its products sales. The company is considering advertising in newspapers and on the Internet. The more the company uses a particular medium, the less effective is each additional ad. The table below shows the number of new customers reached by each ad. Each newspaper ad costs $2,000, and each Internet ad costs $5,000. At most, 45 newspaper ads and 30 Internet ads can be placed.

	Number of Ads	New Customers
Newspapers	1-15	2000
	16-25	1600
	26-35	1100
Internet	1-9	20000
	10-20	18000
	21-35	14000

Formulate a model in standard form to help the company maximize the number of new customers created by advertising. (Note: Don't have to solve it.)

Answer 1

Model of company to maximize the number of new customers created by advertising.

Decision variable:

x_1i=number of newspaper ads

x_2i=number of internet ads

Function objective:

Max z= (1-15) 2000*x₁₁+ (16-25) 2000*x₁₂+ (26-35) 2000*x₁₃+ (1-9) 5000*x₂₁+ (10-20) 5000*x₂₂+ (21-35) 5000*x₂₃

Constraints:

x₁₁+x₁₂+ x₁₃≤ 45

x₂₁+ x₂₂+ x₂₃≤ 30

(1-15) 2000*x₁₁+ (16-25) 2000*x₁₂+ (26-35) 2000*x₁₃+ (1-9) 5000*x₂₁+ (10-20) 5000*x₂₂+ (21-35) 5000*x₂₃ ≤ $225,000

(1-15) 2000*x₁₁ ≤2000

(16-25) 2000*x₁₂ ≤1600

(26-35) 2000*x₁₃ ≤1100

(1-9) 5000*x₂₁ ≤20000

(10-20) 5000*x₂₂ ≤18000

(21-35) 5000*x₂₃ ≤14000

x₁₁, x₁₂, x₁₃, x₂₁, x₂₂, x₂₃ ≥ 0