Question

Ace Trucking Company has an order for delivery of three​products, A,​ B, and C. The table gives the volume in cubic​ feet, the weight in​ pounds, and the value for insurance in dollars for a unit of each of the products. If the carrier can carry 16,400 cubic feet and 16,700 pounds and is insured for $72,500, how many units of each product can be​ carried

Product A Product B Product C

Volume(cu ft) 24 40 80
Weight(lb) 40 30 60
Value ($) 150 190 200

Answer 1

The maximum number of units that can be carried for each product is:
- Product A: 417 units (based on weight)
- Product B: 556 units (based on weight)
- Product C: 362 units (based on insurance value)

Step-by-step explanation:

To determine the number of units of each product that can be carried, we need to compare the available space, weight capacity, and insurance value of the carrier to the requirements of each product. Let's calculate:

1. Calculate the maximum number of units of Product A that can be carried based on volume: 16400 (cubic feet) / 24 (cubic feet per unit) = 683.33 units, rounded down to 683 units.
2. Calculate the maximum number of units of Product B that can be carried based on volume: 16400 (cubic feet) / 40 (cubic feet per unit) = 410 units, rounded down to 410 units.
3. Calculate the maximum number of units of Product C that can be carried based on volume: 16400 (cubic feet) / 80 (cubic feet per unit) = 205 units, rounded down to 205 units.
4. Calculate the maximum number of units of Product A that can be carried based on weight: 16700 (pounds) / 40 (pounds per unit) = 417.5 units, rounded down to 417 units.
5. Calculate the maximum number of units of Product B that can be carried based on weight: 16700 (pounds) / 30 (pounds per unit) = 556.67 units, rounded down to 556 units.
6. Calculate the maximum number of units of Product C that can be carried based on weight: 16700 (pounds) / 60 (pounds per unit) = 278.33 units, rounded down to 278 units.
7. Calculate the maximum number of units of Product A that can be carried based on insurance value: 72500 (dollars) / 150 (dollars per unit) = 483.33 units, rounded down to 483 units.
8. Calculate the maximum number of units of Product B that can be carried based on insurance value: 72500 (dollars) / 190 (dollars per unit) = 381.58 units, rounded down to 381 units.
9. Calculate the maximum number of units of Product C that can be carried based on insurance value: 72500 (dollars) / 200 (dollars per unit) = 362.5 units, rounded down to 362 units.

Therefore, the maximum number of units that can be carried for each product is:

• Product A: 417 units (based on weight)
• Product B: 556 units (based on weight)
• Product C: 362 units (based on insurance value)