1. **Problem Statement:** We are given data on fixed cost, variable cost, total revenue, and units of natural gas delivered to homes. We need to calculate marginal cost (MC) and marginal revenue (MR) for each unit, find the profit-maximizing quantity, determine if the company is making a profit or loss, and recommend an action. 2. **Formulas and Rules:** - Marginal Cost (MC) is the change in total cost when one more unit is produced: $$MC_n = TC_n - TC_{n-1}$$ where $$TC = Fixed\ Cost + Variable\ Cost$$. - Marginal Revenue (MR) is the change in total revenue when one more unit is sold: $$MR_n = TR_n - TR_{n-1}$$. - Profit is maximized where $$MR = MC$$ or just before MR falls below MC. 3. **Calculate Total Cost (TC) for each unit:** Since fixed cost is constant at 75, $$TC_n = 75 + Variable\ Cost_n$$ 4. **Calculate Marginal Cost (MC):** For each unit $$n$$ from 1 to 10, $$MC_n = TC_n - TC_{n-1}$$ 5. **Calculate Marginal Revenue (MR):** For each unit $$n$$ from 1 to 10, $$MR_n = TR_n - TR_{n-1}$$ 6. **Calculations:** | Units | Fixed Cost | Variable Cost | Total Cost (TC) | Total Revenue (TR) | MC = TC_n - TC_{n-1} | MR = TR_n - TR_{n-1} | |-------|------------|---------------|-----------------|--------------------|----------------------|---------------------| | 0 | 75 | 0 | 75 | 0 | - | - | | 1 | 75 | 50 | 125 | 48 | 125 - 75 = 50 | 48 - 0 = 48 | | 2 | 75 | 80 | 155 | 92 | 155 - 125 = 30 | 92 - 48 = 44 | | 3 | 75 | 108 | 183 | 132 | 183 - 155 = 28 | 132 - 92 = 40 | | 4 | 75 | 134 | 209 | 168 | 209 - 183 = 26 | 168 - 132 = 36 | | 5 | 75 | 150 | 225 | 200 | 225 - 209 = 16 | 200 - 168 = 32 | | 6 | 75 | 170 | 245 | 228 | 245 - 225 = 20 | 228 - 200 = 28 | | 7 | 75 | 194 | 269 | 252 | 269 - 245 = 24 | 252 - 228 = 24 | | 8 | 75 | 220 | 295 | 272 | 295 - 269 = 26 | 272 - 252 = 20 | | 9 | 75 | 262 | 337 | 288 | 337 - 295 = 42 | 288 - 272 = 16 | | 10 | 75 | 315 | 390 | 300 | 390 - 337 = 53 | 300 - 288 = 12 | 7. **Profit Maximization:** Profit maximizes where $$MR \geq MC$$ and next unit MR < MC. Check units: - At 5 units: MC = 16, MR = 32 (MR > MC) - At 6 units: MC = 20, MR = 28 (MR > MC) - At 7 units: MC = 24, MR = 24 (MR = MC) - At 8 units: MC = 26, MR = 20 (MR < MC) So, profit-maximizing quantity is 7 units. 8. **Profit or Loss at 7 units:** Profit = Total Revenue - Total Cost = 252 - 269 = -17 (loss) 9. **Recommendation:** Since the company is experiencing a loss at 7 units, it should consider reducing output or adjusting costs/prices. **Final answers:** A. Marginal Cost for units 1 to 10: 50, 30, 28, 26, 16, 20, 24, 26, 42, 53 B. Marginal Revenue for units 1 to 10: 48, 44, 40, 36, 32, 28, 24, 20, 16, 12 C. Profit-maximizing quantity: 7 units D. The company is experiencing a loss at 7 units E. Recommend reducing output or revising strategy