Win Big Gambling Club promotes gambling junkets from a large city to casinos in The Bahamas. The club has budgeted up to $8,000 per week for local advertising. The money is to be allocated among four promotional media: TV spots, newspaper ads, and two types of radio advertisements. Win Big's goal is to reach the largest possible high-potential audience through the various media. The table below presents the number of potential gamblers reached by making use of an advertisement in each of the four media. It also provides the cost per advertisement placed and the maximum number of ads that can be purchased per week.
|
MEDIUM
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AUDIENCE REACHED PER AD
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COST PER AD
|
MAXIMUM ADS PER WEEK
|
|
TV spot (1 minute)
|
5,000
|
$800
|
12
|
|
Daily newspaper (full-page ad)
|
8,500
|
$925
|
5
|
|
Radio spot (30 seconds, prime time)
|
2,400
|
$290
|
25
|
|
Radio spot (1 minute, afternoon)
|
2,800
|
$380
|
20
|
Win Big's contractual arrangements require that at least five radio spots be placed each week. To ensure a broad-scoped promotional campaign, management also insists that no more than $1,800 be spent on radio advertising every week.
a) Formulate a linear programming model for this problem.
b) Set up a spreadsheet model for this problem and use the Excel Solver to find the optimal solution. State the optimal solution and the value of the objective function.