Question 1198755
**1. Find the Total Cost (TC) Equation**

* **Total Cost (TC) = Average Cost (AC) * Quantity (Q)**
* TC = (400/Q + 4 + 0.2Q) * Q
* TC = 400 + 4Q + 0.2Q²

**2. Find the Total Revenue (TR) Equation**

* **Total Revenue (TR) = Price (P) * Quantity (Q)**
* TR = (400 - 2Q) * Q
* TR = 400Q - 2Q²

**3. Find the Profit (π) Equation**

* **Profit (π) = Total Revenue (TR) - Total Cost (TC)**
* π = (400Q - 2Q²) - (400 + 4Q + 0.2Q²)
* π = 400Q - 2Q² - 400 - 4Q - 0.2Q²
* π = 396Q - 2.2Q² - 400

**4. Find the Quantity that Maximizes Profit**

* To find the quantity that maximizes profit, we need to find the derivative of the profit function with respect to Q and set it to zero.
* dπ/dQ = 396 - 4.4Q = 0
* 4.4Q = 396
* Q = 90

**5. Find the Price at Maximum Profit**

* Substitute the optimal quantity (Q = 90) into the demand equation:
* P = 400 - 2 * 90
* P = 400 - 180
* P = $220

**6. Calculate the Maximum Profit**

* Substitute the optimal quantity (Q = 90) into the profit function:
* π = 396 * 90 - 2.2 * 90² - 400
* π = 35640 - 17820 - 400
* π = $17420

**Therefore:**

* **Quantity that maximizes profit:** 90 units
* **Optimal price:** $220
* **Maximum profit:** $17,420