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. if x engines are made, then the unit cost is given by the function $c(x)=x^{2}-520x + 73458$. what is the minimum unit cost? do not round your answer.
unit cost: $

Explanation:

Step1: Find x for minimum cost

For quadratic $C(x)=ax^2+bx+c$, $x=-\frac{b}{2a}$. Here $a=1$, $b=-520$.
$x=-\frac{-520}{2\times1}=260$

Step2: Substitute x into C(x)

Calculate $C(260)=(260)^2 - 520(260)+73458$

Step3: Compute each term

$260^2=67600$, $520\times260=135200$

Step4: Calculate final value

$C(260)=67600-135200+73458=5858$

Answer:

5858