Use the trade discount system shown in the table to calculate the cost of 800 lbs of product if the retail price is $6 per pound.
| | |
| :-------- | :-------------- |
| 0-100 lbs | 10% |
| 101-400 lbs | 20% |
| 401+ lbs | 40% |
Answer (2)
Calculate the cost of the first 100 lbs with a 10% discount: C os t 1 = 100 × 6 × 0.90 = 540 .
Calculate the cost of the next 300 lbs with a 20% discount: C os t 2 = 300 × 6 × 0.80 = 1440 .
Calculate the cost of the remaining 400 lbs with a 40% discount: C os t 3 = 400 × 6 × 0.60 = 1440 .
Calculate the total cost: T o t a lC os t = 540 + 1440 + 1440 = 3420 .
Explanation
Understanding the Problem We need to calculate the total cost of 800 lbs of a product with a retail price of $6 per pound, considering the trade discounts based on quantity. The discounts are 10% for 0 − 100 lbs, 20% for 101 − 400 lbs, and 40% for 401 + lbs.
Calculating Cost for the First 100 lbs First, we calculate the cost for the first 100 lbs. The discount is 10% , so we pay 90% of the retail price for these pounds. C os t 1 = 100 × 6 × ( 1 − 0.10 ) = 100 × 6 × 0.90 = 540
Calculating Cost for the Next 300 lbs Next, we calculate the cost for the next 300 lbs (from 101 to 400 lbs). The discount is 20% , so we pay 80% of the retail price for these pounds. C os t 2 = 300 × 6 × ( 1 − 0.20 ) = 300 × 6 × 0.80 = 1440
Calculating Cost for the Remaining 400 lbs Then, we calculate the cost for the remaining 400 lbs (from 401 to 800 lbs). The discount is 40% , so we pay 60% of the retail price for these pounds. C os t 3 = 400 × 6 × ( 1 − 0.40 ) = 400 × 6 × 0.60 = 1440
Calculating the Total Cost Finally, we sum the costs from each range to find the total cost. T o t a lC os t = C os t 1 + C os t 2 + C os t 3 = 540 + 1440 + 1440 = 3420 Therefore, the total cost for 800 lbs of the product is $3420 .
Examples
Trade discounts are commonly used in business to encourage larger purchases. For example, a local bakery might offer discounts to cafes that buy their bread in bulk. If a cafe buys between 100 and 300 loaves a week, they might get a 15% discount. If they buy more than 300, the discount could increase to 25%. This benefits both the bakery, which secures a large order, and the cafe, which lowers its costs.
The total cost for purchasing 800 lbs of the product is calculated to be $3420, based on the discounts applied at different weight thresholds. Specific calculations include $540 for the first 100 lbs, $1440 for the next 300 lbs, and $1440 for the final 400 lbs. By summing these amounts, we arrive at the final cost.
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