Question

Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when xequalsa. c. Interpret the values obtained in part​ (b). Upper C (x )equals 0.01 x cubed plus 0.2 x squared plus 20 x plus 110​, 0less than or equalsxless than or equals1500​, aequals1000

Answer 1

`C(x)=0.01x^(3) +0.2x^(2) +20x +110`

Average cost:

`(C(x))/(x)=(0.01x^(3) +0.2x^(2) +20x +110)/(x)`

`=0.01x^(2) +0.2x+20+(110)/(x)`

Average cost at x = 1,000

`=0.01(1,000)^(2) +0.2*1,000+20+(110)/(1,000)`

= 10,220.11

`Marginal\ cost=(dC(x))/(dx)`

`= 0.03x^(2) +0.4x+20`

Marginal cost at x = 1,000

`= 0.03(1,000)^(2) +0.4*1,000+20`

= 30,420

Since marginal cost is greater than the average cost, the average cost is increasing.