The daily profit made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. How many cars must be produced per shift for the company to break even?
A) 10 or 40
B) 50
C) 25 or 30
D) None

Question

Quizplus · Accepted Answer

To find the break-even points, set the profit function $P(x) = 0$ and solve for $x$. The equation becomes $-45x^2 + 2250x - 18000 = 0$. Factoring or using the quadratic formula, we find the roots $x = 10$ and $x = 40$, which are the points where the company breaks even.

The Daily Profit Made by an Automobile Manufacturer Is P(x)=−45x2+2,250x−18,000P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000P(x)=−45x2+2,250x−18,000

The Daily Profit Made by an Automobile Manufacturer Is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$