A chair manufacturing company has two different factories. The profit function for Factory I when x chairs are manufactured and sold is as follows: $P ( x ) = - 0.05 x ^ { 2 } + 20 x - 500$ The profit function for Factory II when x chairs are manufactured and sold is as follows: $P ( x ) = - 0.05 x ^ { 2 } + 30 x - 2500$ For what number of chairs is the profit the same at both factories, and what is the profit?
A) 300 chairs; $2000
B) 100 chairs; $1000
C) 0 chairs; $0
D) 200 chairs; $1500

Question

Quizplus · Accepted Answer

To find when the profits are the same, set the profit functions equal: $-0.05x^2 + 20x - 500 = -0.05x^2 + 30x - 2500$. Solving for x gives 200 chairs, and substituting x = 200 into either profit function gives a profit of $1500.

A Chair Manufacturing Company Has Two Different Factories P(x)=−0.05x2+20x−500P ( x ) = - 0.05 x ^ { 2 } + 20 x - 500P(x)=−0.05x2+20x−500

A Chair Manufacturing Company Has Two Different Factories $P ( x ) = - 0.05 x ^ { 2 } + 20 x - 500$