Jacob operates a produce stand on the side of a Florida road. He sells cantaloupes, and baskets of okra,
green beans, and peaches. The number of units of space in the stand each of the produce takes up is 3, 2,
1, and 1, respectively. The stand has a capacity of 100 units. Further, the different produces cost $1, $2,
$2 and $3, respectively for Jacob to purchase. Jacob has a budget of $100. He wants to (i) completely use
his stand space, (ii) completely use his budget, and (iii) stock the stand with exactly half fruit and half
vegetables. We will assume throughout this problem that it is admissible to stock the stand with fractions
of produce/produce baskets.
1. Write a system of linear equations that relates the amounts of different produces in the stand. This
system will have four variables and three constraints.
2. Use Gauss-Jordan elimination to describe all solutions of the system, as a function of the number
of green beans baskets in the stand. (Consider the number of green beans baskets to be the nonbasic
variable.)
3. What would be the composition of the stand if Jacob was insisting on having 24 green beans baskets
in the stand?
4. What is the maximum number of green beans baskets that Jacob can stock in the stand?
5. Suppose that Jacob knows from previous experience that he will be able to sell all of the produce he
stocks his stand with. Suppose he plans on selling the different produce for $3, $4, $3.5 and $3.5,
respectively. What stand composition would help Jacob maximize profit?
