b. Find the marginal cost, marginal revenue, and marginal profit when 70 parkas
are produced and sold using the formulas ,
and .
Marginal cost:
Marginal revenue:
Marginal profit:
c. Use derivatives to estimate the marginal cost, marginal revenue, and marginal
profit when 70 parkas are produced and sold.
Marginal cost:
Marginal revenue:

When calculating the marginal profit, you can find it by subtracting the marginal cost from the marginal revenue. Using the provided values: . Therefore, with a marginal cost of and marginal revenue of , the marginal profit would be . So, the marginal profit is .

To estimate the marginal cost, revenue, and profit using derivatives, recall that the derivative gives the rate of change at a point. If represents the derivative of the cost function, for revenue, and for profit, you’d evaluate these derivatives at . Assuming you’ve derived these functions prior to this, substituting will yield the estimates for marginal cost and marginal revenue at that production level; however, you’ll need their specific expressions to perform the calculation.