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, then the unit cost is given by the function C(x)=0.6x^2-168x+30,389. What is the minimum unit cost?
Do not round your answer.

Answer 1

Answer: $\ 18,629$

Step-by-step explanation:

Given

The unit cost is given by

$C(x)=0.6x^2-168x+30,389$

find the derivative of the unit cost and equate it to zero to obtain the minimum value

$C'(x)=0.6\times 2x-168\\\Rightarrow 0.6\times 2x-168=0\\\Rightarrow 1.2x=168\\\\\Rightarrow x=\dfrac{168}{1.2}\\\\\Rightarrow x=140$

Substitute 140 for $x$ in the cost function, we get

$C(140)=0.6[140]^2-168(140)+30,389\\C(140)=11,760-23,520+30,389\\C(140)=\ 18,629$