Question

An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. Ifx engines are made, then the unit cost is given by the function C(x) = 0.5x ^ 2 - 150x + 26, 777 . How many engines must be made to minimize the unit cost?Do not round your answer.number of airplane engines________

Answer 1

Step-by-step explanation:

We are given the unit cost to produce x number of airplanes as follows;

`C(x)=0.5x^2-150x+26777`

However, to minimize the unit cost, we need to first take the derivative of the cost function and then find its value at zero.

Thuis is shown below;

`C(x)=0.5x^2-150x+26777`
`(d)/(dx)=2(0.5)x^(2-1)-1(150)x^(1-1)+0`

Note that for a derivative, the constant term is always equal to zero. We can now simplify what we have above;

`(d)/(dx)=1x^1-150`
`(d)/(dx)=x-150`

We now set this equal to zero and simplify;

`x-150=0`

Add 150 to both sides;

`x=150`

ANSWER:

Therefore, to minimize the unit cost, 150 engines must be made.