Question 1199609
**i) Find Total Cost (TC) and Total Revenue (TR) functions**

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

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

**ii) Calculate Profit-Maximizing Price and Quantity**

1. **Find Marginal Cost (MC):**
   * MC = d(TC)/dQ = 4 + 0.4Q

2. **Find Marginal Revenue (MR):**
   * MR = d(TR)/dQ = 400 - 4Q

3. **Set MR = MC to find profit-maximizing quantity:**
   * 400 - 4Q = 4 + 0.4Q
   * 396 = 4.4Q
   * Q = 90 units

4. **Find profit-maximizing price:**
   * P = 400 - 2Q 
   * P = 400 - 2 * 90 
   * P = 220

5. **Calculate Maximum Profit:**
   * Profit (π) = TR - TC
   * π = (220 * 90) - (400 + 4 * 90 + 0.2 * 90²) 
   * π = 19800 - (400 + 360 + 1620) 
   * π = 19800 - 2480 
   * π = 17320

**Therefore:**

* **Profit-maximizing quantity (Q): 90 units**
* **Profit-maximizing price (P): $220**
* **Maximum Profit: $17,320**