Question

(( THIS GIVES 50 POINTS )) PLEASE HELP ASAP

Answer 1

Answer:

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

b) the maximum profit is 200 at 11000 cars

Step-by-step 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