Question

The Sea Wharf Restaurant would like to determine the best way to allocate a monthly advertising budget of $2,000 between newspaper advertising and radio advertising. Management decided that at least 25% of the budget must be spent on each type of media and that the amount of money spent on local newspaper advertising must be at least two and a half times the amount spent on radio advertising. A marketing consultant developed an index that measures audience exposure per dollar of advertising on a scale from 0 to 100, with higher values implying greater audience exposure. If the value of the index for local newspaper advertising is 50 and the value of the index for spot radio advertising is 80, how should the restaurant allocate its advertising budget to maximize the value of total audience exposure

Answer 1

Answer:

Explanation is given below

Explanation:

Given that, the total budget for the media is only $1,000 per month.

For the allocation, each type of media would get at least 25% of the budget.

Hence, from the available information, we have the following:

Parameters:

$1000 = Monthly advertising budget

25%= Minimum spending for each type of media

50 = Value of the index for local newspaper advertising

80= Value of the index for spot radio advertising

Decision variables;

x1= Newspaper advertising budget

x2= Radio advertising budget

LP Model;

Maximize Z=50x1+ 80x2

Subject to:x1+ x2≤1000

x1≥ 250

x2≥ 250

x1,x2≥ 0

p.s. OptimumZ=72, 500,

x1=250,

x2=750