A company produces and sells electronic devices per week

MATHEMATICS · Single correct · AoPS · Mathematics · More Inequalities · More Inequalities

Problem

A company produces and sells

x

electronic devices per week, where

0<x<200

. Its weekly revenue (in dollars) is

R(x)=100x-0.5x^{2}

, and its weekly cost is

C(x)=20x+1000

. The profit earned per device is

P(x)=\dfrac{R(x)-C(x)}{x}

. For what number of devices

x

is the profit per device maximized? (a)

80

(b)

32

(c)

45

(d)

100