Cedar Point amusement park management is preparing the park\'s annual promotiona

Question

Cedar Point amusement park management is preparing the park's annual promotional plan for the coming season. Several advertising alternatives exist: newspaper, television, radio, and displays at recreational shows. The information below shows the characteristics associated with each of the advertising alternatives, as well as the maximum number of placements available in each medium. The following table provides the relevant data.

Let X1 = number of newspaper placements, X2 = number of television placements, X3 = number of radio placements, X4 = number of recreational shows Given an advertising budget of $250,000, how many placements should be made in each medium to maximize total audience exposure? What would be the objective function in this problem?

1500X1 + 2200X2 + 750X3 + 150X4 ? 250000

Minimize 1500X1 + 2200X2 + 750X3 + 150X4

Maximize 80X1 + 120X2 + 45X3 + 10X4

Maximize 100X1 + 50X2 + 50X3 + 3X4

1500X1 + 2200X2 + 750X3 + 150X4 ? 250000

Minimize 1500X1 + 2200X2 + 750X3 + 150X4

Maximize 80X1 + 120X2 + 45X3 + 10X4

Maximize 100X1 + 50X2 + 50X3 + 3X4

Maximum num ber 100 50 50 Exposure (1000s] Ad Type Newspaper Television Radin Shuws Cost 1500 2200 750 150 8O 120 45 10

Explanation / Answer

Let X1 = number of newspaper placements

X2 = number of television placements

X3 = number of radio placements

X4 = number of recreational

shows

Maximize 80X1 + 120X2 + 45X3 + 10X4

Subject to: 1500X1 + 2200X2 + 750X3 + 150X4 250000

X1 100

X2 50

X3 50

X4 3

X1, X2, X3, X4 0

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