Question

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio Newspaper Audience per advertisement 100000 18000 40000 Cost per advertisement $1400 $300 $600 Maximum media usage 10 20 10 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. If the promotional budget is limited to $21,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? If required, round your answers to the nearest dollar. Let T = number of television spot advertisements R = number of radio advertisements N = number of newspaper advertisements Budget ($) T = R = N = Total Budget = $ What is the total audience reached? Round your answer to the nearest whole number. By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number.

Answer 1

Let T = number of television spot advertisements R = number of radio advertisements N = number of newspaper advertisements.

Objective function (Z) = 100,000T + 18,000R + 40,000N

Constraints:

(i): T<=10

(ii): R<=20

(iii): N<=10

(iv): R<=0.5*(T+R+N)

(v): T>=0.1*(T+R+N)

(vi): 1400T+300R+600N<=21,200

Lastly all the variables >=0 and should be integers. Solving in excel using the solver function we get the following solution:

	Variable values as computed by excel
T	10
R	4
N	10
				Formula
Z	1,472,000			100,000T + 18,000R + 40,000N
Constraints
10	<=	10		T<=10
4	<=	20		R<=20
10	<=	10		N<=10
4	<=	12		R<=0.5*(T+R+N)
10	>=	2		T>=0.1*(T+R+N)
21,200	<=	21,200		1400T+300R+600N<=21,200

Thus the answers are:

T (number of television spot advertisements) = 10

R (number of radio advertisements) = 4

N (number of newspaper advertisements) = 10

Total budget = $21,200 and budget for TV = (1400*10) = $14,000. For radio = (300*4) = $1,200 and for newspaper = (600*10) = $6,000

Total audience reached = 1,472,000

If $100 were added to the budget then new no. of audience reached will be = 1,478,000 and hence audience contact increase = 1,478,000 - 1,472,000 = 6,000