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A laptop company is choosing which components they want to put into th
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Bunuel
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A laptop company is choosing which components they want to put into th [#permalink] New post  28 Jan 2022, 07:45
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A laptop company is choosing which components they want to put into their next model. This model laptop will sell for $2000, and every additional component will bring the selling price up an additional $200. However, the company predicts that each time they increase the price, the number of sales will drop by around 5% from the base prediction. What is the best number of components to upgrade in order to maximize revenue?

(A) Six
(B) Five
(C) Four
(D) Three
(E) Two


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JerryAtDreamScore
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Re: A laptop company is choosing which components they want to put into th [#permalink] New post  31 Jan 2022, 16:57
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Bunuel wrote:
A laptop company is choosing which components they want to put into their next model. This model laptop will sell for $2000, and every additional component will bring the selling price up an additional $200. However, the company predicts that each time they increase the price, the number of sales will drop by around 5% from the base prediction. What is the best number of components to upgrade in order to maximize revenue?

(A) Six
(B) Five
(C) Four
(D) Three
(E) Two



Breaking Down the Info:

Set the number of increases in price as x. Then the revenue would be \(R = (2000 + 200x)*(1 - 0.05x)\). We could multiply everything out and use the vertex of this parabola to find the maximum point (or use calculus if you prefer ...)

\(R = 2000 - 100x + 200x - 10x^2 = -10x^2 + 100x + 2000\). The vertex is \(-\frac{b}{2a} = \frac{100}{20} = 5\). Thus 5 increases is the optimal point.

Answer: B
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