1. **Problem statement:** Compare the total costs of three offers for purchasing 2,000 fitness bars, considering list price, discounts, transport, packaging, and cash discounts. 2. **Formulas and rules:** - Calculate the price after the delivery discount: $$\text{Price after discount} = \text{List price} \times (1 - \text{Delivery discount rate})$$ - Add transport and packaging costs. - Apply cash discount (Lieferskonto) on the sum of discounted price plus transport and packaging: $$\text{Cash discount amount} = (\text{Price after discount} + \text{Transport} + \text{Packaging}) \times \text{Cash discount rate}$$ - Final price = (Price after discount + Transport + Packaging) - Cash discount amount 3. **Calculations for each offer:** **Offer 1:** - List price = 1250 - Delivery discount = 20% = 0.20 - Cash discount = 2.0% = 0.02 - Transport = 30 - Packaging = 40 Calculate price after delivery discount: $$1250 \times (1 - 0.20) = 1250 \times 0.80 = 1000$$ Sum with transport and packaging: $$1000 + 30 + 40 = 1070$$ Cash discount amount: $$1070 \times 0.02 = 21.4$$ Final price: $$1070 - 21.4 = 1048.6$$ **Offer 2:** - List price = 1125 - Delivery discount = 10% = 0.10 - Cash discount = 0% (none) - Transport = 0 (not mentioned) - Packaging = 65 Price after delivery discount: $$1125 \times (1 - 0.10) = 1125 \times 0.90 = 1012.5$$ Sum with transport and packaging: $$1012.5 + 0 + 65 = 1077.5$$ No cash discount, so final price = 1077.5 **Offer 3:** - List price = 1380 - Delivery discount = 15% = 0.15 - Cash discount = 2.5% = 0.025 - Transport = 40 - Packaging = 0 (not mentioned) Price after delivery discount: $$1380 \times (1 - 0.15) = 1380 \times 0.85 = 1173$$ Sum with transport and packaging: $$1173 + 40 + 0 = 1213$$ Cash discount amount: $$1213 \times 0.025 = 30.325$$ Final price: $$1213 - 30.325 = 1182.675$$ 4. **Conclusion:** - Offer 1 final price: 1048.6 - Offer 2 final price: 1077.5 - Offer 3 final price: 1182.675 The cheapest offer is **Offer 1** with a final price of 1048.6.