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Re: A batch of widgets costs p + 15 dollars for a company to pro [#permalink]
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Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project




A batch of widgets costs p + 15 dollars for a company to produce and each batch sells for p(9 – p) dollars. For which of the following values of p does the company make a profit?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7


Since profit = revenue - cost, or P = R - C, we need to determine a value of p such that revenue > cost. We have that p + 15 = cost and p(9 - p) = revenue. Therefore, the profit is P = p(9 - p) - (p + 15) = 9p - p^2 - p - 15 = -p^2 + 8p - 15.

Notice that the graph of P = -p^2 + 8p - 15 is a parabola that opens downward, so the maximum value is at its vertex. Recall that we can use the formula -b/2a to find the x-value (in this case, the p-value) of the vertex:

p = -b/2a = -8/(2(-1)) = -8/-2 = 4

Answer: B
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