Question

A New York company is planning to decide about advertisements. He invites executives from a local newspaper, a local TV station, and a local radio station to make a presentation.

The newspaper executive claims to be able to provide an audience of 10,000 customers at a cost of $4,000 per ad. The breakdown of audience:

	Male	Female
Young	2000	1000
Senior	4000	3000

The executive from the local TV station claims to provide an audience of 25,000 customers at a cost of $15,000. The breakdown of audience:

	Male	Female
Young	5000	10000
Senior	5000	5000

The executive from the local radio station claims to provide an audience of 15,000 customers at a cost of $6,000. The breakdown of audience:

	Male	Female
Young	4500	7500
Senior	1500	1500

The company has the following policy:
            a. Use at least twice as many radio commercial as newspaper ads
            b. Reach at least 100,000 customers
            c. Reach at least twice as many young people as senior citizens
            d. Make sure that at least 30% of the audience is female.

Available space limits the number of newspaper ads to seven. The company wants to know the optimal number of each type of advertising to purchase to minimize the total cost.

a. Formulate a linear programming model first and then solve this using Excel.

b. Suppose another local radio station approaches and indicates that its commercial can reach 18,000 customers at a cost of $7,500 with a demographic breakdown:

	Male	Female
Young	4000	8000
Senior	2400	3600

If the company considered this station along with other media alternatives, how would this affect the solution?

Answer 1

Answer A)

Excel Formulation:

	News Paper	TV	Radio
Cost	$    4,000.00	$ 15,000.00	$ 6,000.00
Decision Variable	News Paper	TV	Radio
1	0	6
Objective:
Min Cost	40000
Constrain:				Total
Radio & Newspaper	2	0	-1	-4	<=	0
Min. Audience	10000	25000	15000	100000	>=	100000
Young Audience	-11000	-5000	6000	25000	>=	0
Female Audience	1000	7500	4500	28000	>=	0
Newspaper ads limit	1	0	0	1	<=	7

Solution:

No. of newspaper ads =1

No. of commercials on Radio = 6

let 2 = no. of ads on neaspaper y = no. of cids on radio TV station 2= no. of ads on Radio station Objective: min nouo ac + 1500oy & 6000Z cost per addi subject to construins: 7) Use at least twice as many sudio comm. E as newspaper ads. z > 296 200 50 22 Reveh cut least 100,000 customers I louco y + 85000y + 1500oz >1,00,000 audience per ads 3) Reach cut least twice as many young people as senior citizens rro. of senior and . 3000 gC + 15000y + 1 lucuz ? ? Crownac lodowy + 2000 22 nuo. of young crudience es Snoong ito socoy + Govoz >O scanner

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