Question

(( THIS GIVES 50 POINTS )) PLEASE HELP ASAP

A car company’s profit can be modeled by the equation P = –2x^2 + 44x – 42, where P is the profit in millions of dollars and x is the number of cars sold in thousands.
(a.) How many cars are sold when the company breaks even?
(b.) What is the company’s maximum profit? How many cars sold gives the maximum profit?

Answer 1

a) 1000,21000 are the break even number of cars

b) the maximum profit is 200 at 11000 cars

Explanation:

P = –2x^2 + 44x – 42

To break even, P =0

0 = –2x^2 + 44x – 42

Factor

0 = -2( x^2 -22x+21)

0 = -2 ( x-21)(x-1)

Using the zero product property

0 = x-21 0 = x-1

x=21 x=1

Remember that x is the number of cars in thousands

When the profit is maximum is at the vertex

The vertex is 1/2 way between the two zeros

(1+21)/2 = 22/2 = 11

11 cars sold

The maximum profit is

P(11) = –2(11)^2 + 44(11) – 42=--242+484-42=200

The maximum profit is 200