Tom is a habitual shopper at garage sales. Last Saturday he stopped at one where there were several types of used building materials for sale. At the low prices being asked, Tom knew he could resell the items in another town for a gain. Four things stood in his way
He could only make one round trip to resell the goods
His pickup truck bed would hold only 1000 pounds
The pickup truck bed could hold only 70 cubic feet of merchandise
He had only 200 cash
He wants to load his truck with the mix of materials that will yield the greatest profit.
Item Cubic feet per unit Price per unit Weight per unit Can resell for
2 X4 studs 1 .10 5 pounds .80
4 X 8 plywood 3 .50 20 pounds 3.00
Concrete blocks .5 .25 10 pounds .75
In order to determine the mix of materials that will yield the greatest profit for Tom, we need to calculate the profit for each of the available building materials based on their price, weight, and cubic feet.
First, we need to determine how many units of each material Tom can fit in his pickup truck bed based on its weight and cubic feet capacity.
For 2x4 studs:
Cubic feet per unit: 1
Weight per unit: 5 pounds
To calculate the number of units of 2x4 studs he can fit based on cubic feet capacity:
70 cubic feet / 1 cubic feet per unit = 70 units
To calculate the number of units of 2x4 studs he can fit based on weight capacity:
1000 pounds / 5 pounds per unit = 200 units
Tom can only choose the lower value of the two calculations, which is 70 units for 2x4 studs.
For 4x8 plywood:
Cubic feet per unit: 3
Weight per unit: 20 pounds
To calculate the number of units of 4x8 plywood he can fit based on cubic feet capacity:
70 cubic feet / 3 cubic feet per unit = 23.33 units
To calculate the number of units of 4x8 plywood he can fit based on weight capacity:
1000 pounds / 20 pounds per unit = 50 units
Tom can only choose the lower value of the two calculations, which is 23 units for 4x8 plywood.
For concrete blocks:
Cubic feet per unit: 0.5
Weight per unit: 10 pounds
To calculate the number of units of concrete blocks he can fit based on cubic feet capacity:
70 cubic feet / 0.5 cubic feet per unit = 140 units
To calculate the number of units of concrete blocks he can fit based on weight capacity:
1000 pounds / 10 pounds per unit = 100 units
Tom can only choose the lower value of the two calculations, which is 100 units for concrete blocks.
Now, we can calculate the profit for each material based on its price and the number of units that can be loaded into the truck:
For 2x4 studs:
Profit per unit: $0.80
Total profit for 2x4 studs is: 70 units * $0.80 per unit = $56
For 4x8 plywood:
Profit per unit: $3.00
Total profit for 4x8 plywood is: 23 units * $3.00 per unit = $69
For concrete blocks:
Profit per unit: $0.75
Total profit for concrete blocks is: 100 units * $0.75 per unit = $75
Based on the calculations, Tom can make the greatest profit by loading his truck with concrete blocks, which would yield a total profit of $75.
It is important to note that the calculations are based on the provided data. If there are any additional factors or constraints, they should be taken into consideration in order to make an accurate decision.