Advertising Cost-Minimization Linear Programming Problem
is bordered by the three constraint equations and the nonnegativity requirements. An isocost curve shows that costs are minimized at point M, where the total audience exposure and income constraints are binding. With these constraints binding, slack variables SA = Sj = 0. Thus,
10,000R + 20,000TV = 100,000 minus 10,000R + 10,000TV = 80,000 10,000TV = 20,000 TV = 2
10,000R + 20,000(2) = 100,000 10,000R = 60,000 R = 6
The firm should employ six radio advertisements and two television advertisements to minimize costs while still meeting audience exposure requirements. Total cost for such a campaign is $56,000.
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