In planning a sidewalk cafe, it is estimated that if there are 28 tables, the daily profit will be $8 per table and that, if the number of tables is increased by x, the profit per table will be reduced by $\frac { 1 } { 4 }$ x dollars (due to overcrowding). How many tables should be present in order to maximize the profit?
A) 20
B) 30
C) 10
D) can't do the problem without cost information

Question

Quizplus · Accepted Answer

The profit function is $ P(x) = (28 + x)(8 - \frac{1}{4}x) $. To maximize profit, take the derivative, set it to zero, and solve for $ x $. The solution gives $ x = 2 $, so the optimal number of tables is $ 28 + 2 = 30 $.

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