Question

Suppose that a fashion company determines that the​ cost, in​ dollars, of producing x cellphone cases is given by ​C(x)equalsnegative 0.05 x squared plus 55 x. Find StartFraction Upper C (251 )minus Upper C (250 )Over 251 minus 250 EndFraction ​, and interpret the significance of this result to the company. StartFraction Upper C (251 )minus Upper C (250 )Over 251 minus 250 EndFraction equals nothing ​(Simplify your​ answer.) Interpret the significance of this result to the company. Choose the correct answer below. A. It represents the additional cost to produce one more item after making 250 items. B. It represents the additional cost to produce one item after the fixed costs have been paid. C. It represents the average cost per item to produce 250 items. D. It represents the average cost of producing 251 items.

Answer 1

(a)$29.95

(b)A

Explanation:

The​ cost, in​ dollars, of producing x cellphone cases is given by:

`C(x)=-0.05 x^2+55 x.`

We are required to evaluate:
`(C(251)-C(250))/(251-250)`

`C(251)=-0.05(251)^2+55(251)=10654.95\\C(250)=-0.05(250)^2+55(250)=10625\\\text{Therefore:}\\\\(10654.95-10625)/(251-250)=29.95`

`(C(251)-C(250))/(251-250)=\$29.95`

The value calculated above represents the additional cost to produce one more item after making 250 items.