The daily profit in dollars 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 maximize its profit?
A) 20
B) 25
C) 35
D) 30

Question

Quizplus · Accepted Answer

The maximum profit occurs at the vertex of the parabola represented by the quadratic equation. The x-coordinate of the vertex can be found using the formula $x = -\frac{b}{2a}$, where $a = -45$ and $b = 2250$. Plugging these values in gives $x = -\frac{2250}{2(-45)} = 25$.

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