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.

Question

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nuuk nuuk · Answer 1 · 2021-05-13T04:28:05+02:00

Answer: [tex]\$18,629[/tex]

Step-by-step explanation:

Given

The unit cost is given by

[tex]C(x)=0.6x^2-168x+30,389[/tex]

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

[tex]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[/tex]

Substitute 140 for [tex]x[/tex] in the cost function, we get

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