Question

An alrcraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. If

x engines are made, then the unit cost is given by the function C(x)=0.9x - 306x +36,001. What is the minimum unit cost?

Do not round your answer.

Answer 1

C(x) should be ;

C(x)=0.9x² - 306x +36,001

Answer:

$9991

Explanation:

Given :

C(x)=0.9x^2 - 306x +36,001

To obtain minimum cost :

Cost is minimum when, C'(x) = 0

C'(x) = 2(0.9x) - 306 = 0

C'(x) = 1.8x - 306 = 0

1.8x - 306 = 0

1.8x = 306

x = 306 / 1.8

x = 170

Hence, put x = 170 in C(x)=0.9x²- 306x +36,001 to obtain the

C(170) = 0.9(170^2) - 306(170) + 36001

C(170) = 26010 - 52020 + 36001

= 9991

Minimum unit cost = 9991