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ICE Princess25 [194]
3 years ago
14

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

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
8 0

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.

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