Question

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made in the unit cost is given by the function C(x)=x^2-520x+79,797. What is the minimum unit cost? Do not round your answer.

Answer 1

The minimum unit cost is $12,197.

Explanation:

The cost function is given below:

`C\mleft(x\mright)=x^2-520x+79,797`

To find the minimum unit cost, first, find the derivative of C(x).

`C^(\prime)(x)=2x-520`

Next, set the derivative equal to 0 and solve for x.

`\begin{gathered} 2x-520=0 \\ 2x=520 \\ x=520/2 \\ x=260 \end{gathered}`

Finally, substitute x=260 into C(x) to find the minimum cost.

`\begin{gathered} C\mleft(x\mright)=x^2-520x+79,797 \\ \implies C(260)=(260)^2-520(260)+79,797 \\ =67600-135,200+79,797 \\ =12,197 \end{gathered}`

The minimum unit cost is $12,197.