Question 1198187
**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.