Question

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

Suppose the marginal cost for the ACME Corporation for producing Wylie Rocket Fuel is given by the equation:
MC(q) = 200 * (q + 9)^-.5,
where q is quantity produced in gallons, and marginal cost is in Simoleons ($) per Gallon. Also suppose ACME has fixed costs of $4000.
1. Find the total cost of producing 91 units of ACME rocket fuel.

Answer 1

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

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.