Solve the problem.
-The price p (in dollars) and the quantity x sold of a certain product obey the demand equation $$p = - 10 x + 240 , \quad 0 \leq x \leq 24$$ What price should the company charge to maximize revenue?
A) $6
B) $18
C) $14.4
D) $12

Question

Quizplus · Accepted Answer

Revenue is maximized when the derivative of the revenue function with respect to x is zero. Revenue R is given by R = p(x) * x = (-10x + 240)x. Differentiating R with respect to x and setting it to zero gives -20x + 240 = 0, solving for x gives x = 12. Substituting x = 12 into the demand equation gives p = -10(12) + 240 = $120.

Solve the Problem p=−10x+240,0≤x≤24p = - 10 x + 240 , \quad 0 \leq x \leq 24p=−10x+240,0≤x≤24

Solve the Problem $p = - 10 x + 240 , \quad 0 \leq x \leq 24$