A linear programming computer package is needed.

Suppose a seafood company is a buyer and distributor of seafood products that are sold to restaurants and specialty seafood outlets throughout the Northeast. The company has a frozen storage facility in New York City that serves as the primary distribution point for all products. One of the company's products is frozen large black tiger shrimp, which are sized at $1620$ pieces per pound. Each Saturday the company can purchase more tiger shrimp or sell the tiger shrimp at the existing New York City warehouse market price. The company's goal is to buy tiger shrimp at a low weekly price and sell it later at a higher price. The company currently has $20,000$ pounds of tiger shrimp in storage. Space is available to store a maximum of $100,000$ pounds of tiger shrimp each week. In addition, the company developed the following estimates of tiger shrimp prices for the next four weeks.

Week Price$/$lb

$1$ $$6\mathrm{.}05$

$2$ $$6\mathrm{.}25$

$3$ $$6\mathrm{.}75$

$4$ $$5\mathrm{.}60$

The company would like to determine the optimal buying$-$storing$-$selling strategy for the next four weeks. The cost to store a pound of shrimp for one week is $$0\mathrm{.}15,$ and to account for unforeseen changes in supply or demand, management also indicated that $25,000$ pounds of tiger shrimp must be in storage at the end of week $4.$

$($a$)$

Determine the optimal buying$-$storing$-$selling strategy for the company.

Week Bought $($in lb$)$ Sold $($in lb$)$ Store $($in lb$)$

$1$

$2$

$3$

$4$

$($b$)$

What is the contribution to profit during the four$-$weeks $($in $$)?$