Question

An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function:P(x) = -10x2 + 3500x – 66,000, where P(x) is the profit in dollars and x is the number of automobiles made and sold. How many cars should be made and sold to maximize profit?

Answer 1

Answer:  175

Step-by-step explanation:

To find maximum, we need to find the vertex.  

The x-value of the vertex is the number of automobiles that should be made and sold.  The y-value is the maximum profit.

P(x) = -10x² + 3500x - 66,000

         a=-10, b = 3500, c=-66,000

$x=\dfrac{-b}{2a}$

$x=\dfrac{-(3500)}{2(-10)}$

$x = \dfrac{-3500}{-20}$

$x = 175$

BONUS:

The maximum profit is: P(x) = -10(175)² + 3500(175) - 66,000

                                              = -300,625 + 612,500 - 66,000

                                              = 245,875