Question

A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day is given by ​C(x)equals350plus2xminus0.01x squared for 0less than or equalsxless than or equals100. Find the marginal cost at a production level of 70 dozen pens and interpret the result.

Answer 1

0.6

Step-by-step explanation:

Given that the manufacturer has a total cost in dollars of producing x dozen pens in one day given by

`C(x)=350+2x-0.01x^(2)`

Marginal cost is the derivative of the total cost function with respect to the output variable which is x here.

MC = C'(x)

= 2 - 2 × 0.01x

MC = 2 - 0.02x

MC at a production level of 70 dozen pens is:

MC (x = 70) = 2 - 0.02 × 70

= 2 - 1.4

= 0.6

Therefore, marginal cost at a production level of 70 dozen pens is 0.6.