The Sea Wharf Restaurant would like to determine the best wa

The Sea Wharf Restaurant would like to determine the best way to allocate a monthly advertising budget of $1000 between newspaper advertising and radio advertising. Management decided that at least 25 percent 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 twice 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? a. Formulate a linear programming model that can be used to determine how the restaurant should allocate its advertising budget in order to maximaize the value of total audience exposure. b. Solve the problem using the graphical solution procedure.

Solution

Objective Function: MAX = X1(newspaperValueIndex) + X2(radioValueIndex)

Constraints: X1 >= 0.25(Budget)

X2 >= 0.25(Budget) X1 >= 2(X2)

Where: - X1 – Dollars spent on Newspaper advertisement.

- X2 – Dollars spent on Radio advertisement.

- Budget = $1,000.00

- newspaperValueIndex = 50

- radioValueIndex = 80

A.) MAX 50(X1) + 80(X2) s.t. X1 + X2 = 1,000 X1 >= 250 X2 >= 250 X1 >= 2(X2)

B.) (obtained from Lingo output) X1 = 666.67; X2 = 333.33; Audience Exposure = 60,000