High School

For a cost function \( C(x) = 60000 + 60x + 70400x^2 \), measured in dollars, find the marginal cost at the production level \( x = 80 \).

Provide the value of the marginal cost at \( x = 80 \).

Answer :

Final answer:

The marginal cost at x = 80 is $70,460.

Explanation:

The marginal cost represents the change in cost for producing one additional unit of a product. To find the marginal cost at x = 80, we need to find the derivative of the cost function. Taking the derivative of C(x) = 60000 + 60x + 70400x with respect to x gives us:

  • C'(x) = 60 + 70400

Substituting x = 80 into the derivative:

  • C'(80) = 60 + 70400
  • C'(80) = 70460

Consequently, $70,460 is the marginal cost when x = 80.

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