Question

Suppose that the marginal cost function of a handbag manufacturer is C'(x) = 0.375x² - x + 500 dollars per unit at production level x (where x is measured in units of 100 handbags). Find the total cost of producing 10 additional units if 8 units are currently being produced. Total cost of producing the additional units: ___

Note: Your answer should be a dollar amount and include a dollar sign and be correct to two decimal places.

Answer 1

$5535.00

Explanation:

You want the cost to produce 10 more units if 8 are being produced and the marginal cost function is c'(x) = 0.375x² -x +500.

Cost

The cost is the integral of the marginal cost. If we want 10 more units than the 8 being produced, the total cost for those units will be the definite integral of the marginal cost function from 8 to (8+10) = 18.

The attachment shows that integral to have a value of 5535.

The cost to produce 10 more units is $5535.00.

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Additional comment

Many graphing calculators can do the numerical integration for you. The integral of the function is ...

C(x) = x³/8 -x²/2 +500x

The cost of interest is C(18) -C(8).