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
