Question

Recall Marginal Cost is the derivative of Total Cost, and Fixed Cost is the cost of producing zero units.

Answer 1

Answer:

The total cost of producing 91 units of ACME rocket fuel is $3999.99.

Step-by-step explanation:

The Marginal Cost is given by the following function

$MC(q) = 200*(q+9)^{-5}$

The total cost function is the integrative of the marginal cost function. So:

$TC(q) = \int {MC(q)} \, dq$

$TC(q) = \int {200*(q+9)^{-5}} \, dq$

$TC(q) = -50*(q+9)^{-4} + K$

In which K, the integrative constant, is the fixed cost. So $K = 4000$.

1. Find the total cost of producing 91 units of ACME rocket fuel.

This is TC(91).

So

$TC(91) = -50*(91+9)^{-4} + 4000 = 3999.99$

The total cost of producing 91 units of ACME rocket fuel is $3999.99.