Tom Is a Habitual Shopper at Garage Sales State the Decision Variables (Give Them Labels)

Essay

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.
$\begin{array}{|c|c|c|c|c|}\hline \text { Item } & \text { Cubic feet per } & \text { Price per unit } &\text { Weight per } & \text { Can resell for } \\&\text { Item } &&\text { Item } \\\hline 2 \times 4 \text { studs } & 1 & \$ 0.10 & 5 \text { pounds } & \$ 0.80\\\hline 4 \times 8 \text { plywood } & 3 & \$ 0.50 & 20 \text { pounds } & \$ 3.00 \\\hline \text { Concrete blocks } & 0.5 & \$ 0.25 & 10 \text { pounds } & \$ 0.75 \\\hline\end{array}$ State the decision variables (give them labels). State the objective function. Formulate the constraints of this problem. Do not solve, but speculate on what might be a good solution for Tom. You must supply a set of quantities for the decision variables. Provide a sentence or two of support for your choice.