1. **Problem Statement:** Juan runs a hotdog stand with the following details: - Price per sandwich: 50 - Discount for customers with own container (20% of customers): 2 - Variable cost per sandwich: 22 - Fixed costs per month: 10,000 We need to find: 1. Contribution margin per sandwich 2. Break-even point in number of sandwiches 3. Break-even point in sales pesos 4. Profit if 500 sandwiches are sold 2. **Contribution Margin per Sandwich:** Contribution margin is the amount each unit contributes to covering fixed costs and profit. Since 20% of customers get a 2 discount, average price per sandwich is: $$\text{Average price} = 0.8 \times 50 + 0.2 \times (50 - 2) = 0.8 \times 50 + 0.2 \times 48 = 40 + 9.6 = 49.6$$ Variable cost per sandwich is 22. Contribution margin per sandwich: $$\text{CM} = \text{Average price} - \text{Variable cost} = 49.6 - 22 = 27.6$$ 3. **Break-Even Point in Number of Sandwiches:** Break-even point (BEP) is where total contribution covers fixed costs: $$\text{BEP units} = \frac{\text{Fixed costs}}{\text{Contribution margin}} = \frac{10000}{27.6} \approx 362.32$$ Since Juan can't sell a fraction of a sandwich, he needs to sell at least 363 sandwiches. 4. **Break-Even Point in Sales Pesos:** Sales at break-even point: $$\text{BEP sales} = \text{BEP units} \times \text{Average price} = 362.32 \times 49.6 \approx 17951.5$$ 5. **Profit if 500 Sandwiches are Sold:** Total contribution from 500 sandwiches: $$500 \times 27.6 = 13800$$ Profit is total contribution minus fixed costs: $$\text{Profit} = 13800 - 10000 = 3800$$ **Final answers:** - Contribution margin per sandwich = 27.6 - Break-even point in sandwiches = 363 - Break-even point in sales pesos = 17951.5 - Profit at 500 sandwiches = 3800