Use the trade discount system shown in the table to calculate the cost of $1,000 lbs$ of product if the retail price is $5 per pound.
| Trade Discount |
|:-------------------------------------------------------:|
| 0-100 lbs | 10 % |
| 101-400 lbs | 20 % |
| 401+ lbs | 40 % |
Answer (2)
Calculate the cost for the first 100 lbs with a 10% discount: cos t 1 = 100 × 5 × ( 1 − 0.10 ) = 450 .
Calculate the cost for the next 300 lbs (101-400 lbs) with a 20% discount: cos t 2 = 300 × 5 × ( 1 − 0.20 ) = 1200 .
Calculate the cost for the remaining 600 lbs (401-1000 lbs) with a 40% discount: cos t 3 = 600 × 5 × ( 1 − 0.40 ) = 1800 .
Sum the costs to find the total cost: T o t a lC os t = 450 + 1200 + 1800 = 3450 . The total cost is 3450 .
Explanation
Understanding the Problem We need to calculate the total cost of 1000 lbs of product given the retail price and the trade discount system. The retail price is $5 per pound, and the discounts vary based on the quantity purchased.
Calculating Cost for 0-100 lbs First, let's calculate the cost for the first 100 lbs. The price per pound is $5, and there's a 10% discount. So, the cost for this range is: cos t 1 = 100 × 5 × ( 1 − 0.10 ) cos t 1 = 100 × 5 × 0.90 cos t 1 = 450
Calculating Cost for 101-400 lbs Next, let's calculate the cost for the range of 101-400 lbs. This is a total of 300 lbs (400 - 100 = 300). The price per pound is $5, and there's a 20% discount. So, the cost for this range is: cos t 2 = ( 400 − 100 ) × 5 × ( 1 − 0.20 ) cos t 2 = 300 × 5 × 0.80 cos t 2 = 1200
Calculating Cost for 401-1000 lbs Now, let's calculate the cost for the range of 401-1000 lbs. This is a total of 600 lbs (1000 - 400 = 600). The price per pound is $5, and there's a 40% discount. So, the cost for this range is: cos t 3 = ( 1000 − 400 ) × 5 × ( 1 − 0.40 ) cos t 3 = 600 × 5 × 0.60 cos t 3 = 1800
Calculating Total Cost Finally, let's add up the costs from each range to find the total cost: T o t a lC os t = cos t 1 + cos t 2 + cos t 3 T o t a lC os t = 450 + 1200 + 1800 T o t a lC os t = 3450 Therefore, the total cost for 1000 lbs of product is $3450.
Examples
Trade discounts are commonly used by suppliers to encourage larger orders from retailers. For example, a local farm might offer discounts to grocery stores based on the volume of produce they purchase. This helps the farm sell more of its product and allows the grocery store to increase its profit margin. Understanding how to calculate costs with trade discounts is essential for businesses to manage their expenses and pricing strategies effectively.
The total cost of 1,000 lbs of product at $5 per pound with trade discounts is calculated to be $3,450. The calculations involve applying a 10% discount for the first 100 lbs, a 20% discount for the next 300 lbs, and a 40% discount for the remaining 600 lbs. Finally, the costs from each range are summed up to reach the total cost.
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