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

question 72

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.
$\begin{array}{|l|c|c|c|c|}\hline \text { Cubic feet per } && \text { Weight per } \\\text { Item }&\text { unit }&\text { Price per unit }&\text { unit }&\text { Can resell for }\\\hline 2\times4 \text { studs } & 1 & \$ 0.10 & 5 \text { pounds } & \$ 0.80 \\\hline 4 \times 8 \text { plywood } & 3 & \$ 0.50 & 20 \text { pounds } & \$ 3.00 \\\hline \text { Concrete blocks } & 0.5 & \$ 0.25 & 10 \text { pounds } & \$ 0.75 \\\hline\end{array}$
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.

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Definitions:

Parallelogram Steering

A steering linkage design in many vehicles where the linkage forms a parallelogram, allowing the wheels to move parallel to each other during turns.

Linkage Components

Various mechanical parts that connect together to transmit motion in order to perform a specific task.

Tie-rods

Components in a vehicle's steering system that help transfer the movement from the steering rack or center link to the steering knuckle, thus making the wheels turn.

Power Steering Hoses

High-pressure hoses that convey hydraulic fluid between the power steering pump and the steering gear to assist in vehicle steering.