Question 1198187: Basic calculus
The selling price of a particular type of car is $20,000. The total cost of producing the car is TC = 2000 + X2.
A. Find the marginal revenue function?
B. Find the marginal cost function?
C. Find the quantity that maximizes profit?
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! **A. Find the Marginal Revenue Function**
* **Revenue (R):**
* Revenue is the selling price per unit multiplied by the number of units sold.
* R(X) = Selling Price * Quantity = $20,000 * X
* R(X) = $20,000X
* **Marginal Revenue (MR):**
* Marginal Revenue is the derivative of the revenue function with respect to the quantity.
* MR(X) = dR(X)/dX = d/dX ($20,000X) = $20,000
**B. Find the Marginal Cost Function**
* **Marginal Cost (MC):**
* Marginal Cost is the derivative of the total cost function with respect to the quantity.
* MC(X) = dTC(X)/dX = d/dX (2000 + X^2) = 2X
**C. Find the Quantity that Maximizes Profit**
* **Profit (P):**
* Profit is the difference between revenue and total cost.
* P(X) = R(X) - TC(X) = $20,000X - (2000 + X^2)
* P(X) = $20,000X - 2000 - X^2
* **To maximize profit, find the quantity (X) where the marginal revenue equals the marginal cost:**
* MR(X) = MC(X)
* $20,000 = 2X
* X = 10,000
**Therefore:**
* The marginal revenue function is MR(X) = $20,000.
* The marginal cost function is MC(X) = 2X.
* The quantity that maximizes profit is 10,000 units.
|
|
|
