A local pub specializing in small craft-brews is trying to figure out how many d

Question

A local pub specializing in small craft-brews is trying to figure out how many different beers to carry. They estimate every tap added will increase revenue, but with diminishing returns: each tap will increase profits by 20% less than the tap before. Revenue from the first tap is $10,000, adding the second is $10,000+$8000 =$18,000, the third tap is $18,000+$6,400=$24,400, and so on. If the fixed costs of the bar are $30,000 and each tap costs $400, how many taps should the bar install to maximize profit?

A. The pub will never be profitable.

B. 10

C. 15

D. 20 or more

Explanation / Answer

The bar will install 15 taps to maximize the profit. This is because the bar will stop adding tap when the profit from tap is less than the additional cost of installing the tap. When the bar will add 16th tap the additional cost will be $400 but additional profit from 16th tap will be 351.85 which is less than 400. So the bar will install 15 taps to maximize the profit.

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