Define variables for buying, selling, and inventory held in each week.

The Atlantic Seafood Company (ASC) is a buyer and distributor of seafood products that are sold to restaurants and specialty seafood outlets throughout the Northeast. ASC has a frozen storage facility in New York City that serves as the primary distribution point for all products. One of the ASC products is frozen large black tiger shrimp, which are sized at 16 to 20 pieces per pound. Each Saturday, ASC can purchase more tiger shrimp or sell the tiger shrimp at the existing New York City warehouse market price. ASC’s goal is to buy tiger shrimp at a low weekly price and sell it later at a higher price. ASC 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, ASC developed the following estimates of tiger shrimp prices for the next four weeks:

ASC 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 $0.15, 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. Determine the optimal buying/storing/selling strategy for ASC. What is the projected four-week profit? (Hint: Define variables for buying, selling, and inventory held in each week. Then use a constraint to define the relationship between these: inventory from end of previous period 1bought this period 2sold this period 5inventory at end of this period. This type of constraint is referred to as an inventory balance constraint.)

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