1. **Stating the problem:** We have three potential locations (A, B, C) for a cake company's new outlet, each with different fixed costs (FC), variable costs per unit (VC), and the same selling price per unit (P). We need to determine: a. Which location is best for production plans of 800 units and 1600 units. b. The break-even point (BEP) for each location. 2. **Given data:** - Location A: $FC=13000000$, $VC=68000$, $P=88000$ - Location B: $FC=18000000$, $VC=63000$, $P=88000$ - Location C: $FC=23000000$, $VC=58000$, $P=88000$ 3. **Formulas and rules:** - Total Cost (TC) = Fixed Cost + Variable Cost per unit $ \times $ Quantity $$TC = FC + VC \times Q$$ - Total Revenue (TR) = Price per unit $ \times $ Quantity $$TR = P \times Q$$ - Profit = TR - TC - Break-Even Point (BEP) in units is where Profit = 0, so: $$BEP = \frac{FC}{P - VC}$$ 4. **Calculate profit for each location at 800 units:** - Location A: $$TC_A = 13000000 + 68000 \times 800 = 13000000 + 54400000 = 67400000$$ $$TR_A = 88000 \times 800 = 70400000$$ $$Profit_A = 70400000 - 67400000 = 3000000$$ - Location B: $$TC_B = 18000000 + 63000 \times 800 = 18000000 + 50400000 = 68400000$$ $$TR_B = 88000 \times 800 = 70400000$$ $$Profit_B = 70400000 - 68400000 = 2000000$$ - Location C: $$TC_C = 23000000 + 58000 \times 800 = 23000000 + 46400000 = 69400000$$ $$TR_C = 88000 \times 800 = 70400000$$ $$Profit_C = 70400000 - 69400000 = 1000000$$ 5. **Calculate profit for each location at 1600 units:** - Location A: $$TC_A = 13000000 + 68000 \times 1600 = 13000000 + 108800000 = 121800000$$ $$TR_A = 88000 \times 1600 = 140800000$$ $$Profit_A = 140800000 - 121800000 = 19000000$$ - Location B: $$TC_B = 18000000 + 63000 \times 1600 = 18000000 + 100800000 = 118800000$$ $$TR_B = 88000 \times 1600 = 140800000$$ $$Profit_B = 140800000 - 118800000 = 22000000$$ - Location C: $$TC_C = 23000000 + 58000 \times 1600 = 23000000 + 92800000 = 115800000$$ $$TR_C = 88000 \times 1600 = 140800000$$ $$Profit_C = 140800000 - 115800000 = 25000000$$ 6. **Determine the best location based on profit:** - At 800 units: Location A has highest profit (3000000). - At 1600 units: Location C has highest profit (25000000). 7. **Calculate BEP for each location:** - Location A: $$BEP_A = \frac{13000000}{88000 - 68000} = \frac{13000000}{20000} = 650$$ - Location B: $$BEP_B = \frac{18000000}{88000 - 63000} = \frac{18000000}{25000} = 720$$ - Location C: $$BEP_C = \frac{23000000}{88000 - 58000} = \frac{23000000}{30000} \approx 767$$ **Final answers:** - a. Best location for 800 units: Location A - a. Best location for 1600 units: Location C - b. BEP units: Location A = 650, Location B = 720, Location C = 767