6. (20 pts) Integer programming. AMP Chapter 9 problem 3. Write down the integer

Question

6. (20 pts) Integer programming. AMP Chapter 9 problem 3. Write down the integer programming formulation of the problem and solve the problem using the optimization software of your choice The marketing group of A. J. Pitt Company is considering the options available for its next advertising campaign program. After a great deal of work, the group has identified a selected number of options with the characteristics shown in the accompanying table Total Trade ar motiona resource IVmagazine Newspaper Radio magaztne campaign avatlable Customers reached 1,000,000 200,000 300,000 400,000 450,000 450,000 Cost (S) Designers needed (man-hours) Salesmen needed (man-hours) 500,000 150,000 300,000 250,000 250,000 100,000 1,800,000 700 250 200 300 400 1,500 200 100 100 100 100 1,000 1,200 The objective of the advertising program is to maximize the number of customers reached, subject to the limitation of resources (money, designers, and salesman) given in the table above. In addition, the following constraints have to be met: i) If the promotional campaign is undertaken, it needs either a radio or a popular magazine campaign effort to support it. i) The firm cannot advertise in both the trade and popular magazines.Formulate an integer-programming model that will assist the company to select an appropriate advertising campaign strategy

Explanation / Answer

Decision variable:

Let, Xi = 1 if ith advertising program is selected otherwise, X1 =0

Where,

i =1, 2,

Variable TV Trade Maz. Newspaper Radio Popular Maz Promotional Campaign

i 1 2 3 4 5 6

Objective function:

Objective is to maximize the customer reach:

Max Z = 1,000,000*X1 + 200,000*X2 + 300,000*X3 + 400,000*X4 + 450,000*X5 + 450,000*X6

Subject to:

Cost of program and budget available:

$500,000*X1 + $150,000*X2 + $300,000*X3 + $250,000*X4 + $250,000*X5 + $100,000*X6 <= $1,800,000

Designers man-hours needed and available:

700*X1 + 250*X2 + 200*X3 + 200*X4 + 300*X5 + 400*X6 <= 1500

Salesmen man-hours needed and available:

200*X1 + 100*X2 + 100*X3 + 100*X4 + 100*X5 + 1000*X6 <= 1200

If the promotional campaign is under taken, it needs either a radio or popular magazine

X6 = X2 + X5

X6 - X2 - X5 = 0

The firm cannot advertise in both the trade and popular magazines:

X2 + X3 <= 1

All Xi are binary integer variable

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