Tom is a habitual shopper at garage sales. Last Saturday he stopped at one where
ID: 456290 • Letter: T
Question
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 that he could resell the items in another town for a substantial 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 at most 70 cubic feet of merchandise; and he had only $200 cash with him. He wants to load his truck with the mix of materials that will yield the greatest profit when he resells them.
Item
Cubic feet per unit
Price per unit
Weight per unit
Can resell for
2 x 4 studs
1
$0.10
5 pounds
$0.80
4 x 8 plywood
3
$0.50
20 pounds
$3.00
Concrete blocks
0.5
$0.25
10 pounds
$0.75
Algebraically state the objective and constraints of this problem.
Item
Cubic feet per unit
Price per unit
Weight per unit
Can resell for
2 x 4 studs
1
$0.10
5 pounds
$0.80
4 x 8 plywood
3
$0.50
20 pounds
$3.00
Concrete blocks
0.5
$0.25
10 pounds
$0.75
Explanation / Answer
Studs
Maximum attainable profit is
70 * 0.70 = $49.00
Plywood
Maximum attainable profit is = 23.33*2.50 = $58.33
Concrete blocks
Maximum quantity = 100.100 * 0.50 = $50
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