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7 September, 10:04

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

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  1. 7 September, 13:20
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    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
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