Question

The cost to produce q items is C(q) = 900 + 5q² dollars.

Find the marginal cost of producing the 10th item. Interpret your answer in terms of costs.
The marginal cost of producing the 10th item is $______

Answer 1

To find the marginal cost of producing the 10th item, we need to calculate the change in total cost divided by the change in quantity. The cost function is C(q) = 900 + 5q² dollars. The marginal cost is $280.

Step-by-step explanation:

To find the marginal cost of producing the 10th item, we need to calculate the change in total cost divided by the change in quantity. The cost function given is C(q) = 900 + 5q² dollars. Since we want to find the marginal cost for the 10th item, we need to find C(10) - C(9).

Substituting q = 10 into the cost function, we get C(10) = 900 + 5(10)² = 1450 dollars.

Substituting q = 9 into the cost function, we get C(9) = 900 + 5(9)² = 1170 dollars.

Therefore, the marginal cost of producing the 10th item is C(10) - C(9) = 1450 - 1170 = 280 dollars.