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 × 4 studs 1 $0.10 5 pounds $0.80
4 × 8 plywood 3 $0.50 20 pounds $3.00
Concrete blocks 0.5 $0.25 10 pounds $0.75

Formulate this problem as a linear program.

Let S be the number of studs purchased
Let P be the number of plywood units purchased
Let C be the number of concrete blocks purchased

Maximize profit = $0.70S + $2.50P + $0.50C
Subject to
5S + 20P + 10C ? 1000
S + 3P + 0.5C ? 70
$0.10S + $0.50P + $0.25C ? $200
S, P, C ? 0