Tom Is a Habitual Shopper at Garage Sales

question 15

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.
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:

Crossed-aldol Product

The product resulting from an aldol reaction between two different aldehyde or ketone reactants, occasionally leading to complex mixtures.

2,2-dimethylpropanal

A chemical compound, specifically an aldehyde, characterized by the presence of two methyl groups attached to the second carbon in a propane chain.

Propanal

An organic compound with the formula CH3CH2CHO, a type of aldehyde that is used as an intermediate in organic synthesis.

Butanal

An aldehyde with the formula C4H8O, it is a four-carbon chain compound with a carbonyl group attached to the first carbon.