Question
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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:

Ask by Collins Fernandez. in the United States
Nov 06,2024

Upstudy AI Solution

Tutor-Verified Answer

Answer

Marginal profit when 70 parkas are produced and sold is $-1.2. For marginal cost and revenue using derivatives, we need the specific functions for cost and revenue.

Solution

To find the marginal profit when 70 parkas are produced and sold, we can use the formula for marginal profit:
Given:
  • Marginal Cost = $0.8
  • Marginal Revenue = $-0.4
Now, we can calculate the marginal profit:
So, the marginal profit when 70 parkas are produced and sold is:

Part c: Using Derivatives

To estimate the marginal cost, marginal revenue, and marginal profit using derivatives, we need the functions for cost , revenue , and profit .
  1. Marginal Cost: This is the derivative of the cost function with respect to :
  2. Marginal Revenue: This is the derivative of the revenue function with respect to :
  3. Marginal Profit: This is the derivative of the profit function with respect to :
To provide numerical values for the marginal cost and marginal revenue using derivatives, we would need the specific functions and . If you have those functions, please provide them, and I can help you calculate the derivatives at . If not, we can only state the formulas as shown above.

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Extra Insights

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.

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