QUESTION 1 The ASC is a buyer and distributor of seafood products that are sold

Question

QUESTION 1 The 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 sizeable black shrimp. Each Saturday ASC can purchase more tiger shrimp or sell the tiger shrimp at the existing New York City warehouse market price. The ASC goal is to buy tiger shrimp at a low weekly price and sell it later at a higher price. ASC currently has 100 pounds of tiger shrimp in storage. Space is available to store a maximum of 600 pounds of tiger shrimp each week. Also, ASC developed following estimates of tiger shrimp prices for the next two weeks Week1 Price $ 10.00 9.00 $9.00 ASC would like to determine the optimal buying-storing-selling strategy for the next two weeks. The cost to store a pound of shrimp for one week is $10, and management indicated that at least 200 pounds of tiger shrimp must be in storage at the end of week 2. a) Define the decision variables. (3 points) b) Define the objective function. (2 points) ) Define the constraints (5 points)

Explanation / Answer

a. The decision variables will be: x1 = quantity of shrimps purchased in week 1, x2 = quantity of shrimps purchased in week 2, y1 = quantity of shrimps sold in week 1 and y2 = quantity of shrimps sold in week 2.

b. Objective is to maximize the profit.

Total sales amount = 10x1+9x2. Total purchase amount = 10y1+9y2

Ending inventory after 1 week = 100+x1-y1. Thus cost of storage for week 1 = $10*(100+x1-y1)

Ending inventory for week 2 = 100+x1-y1+x2-y2. Thus storage cost for week 2 = $10*(100+x1-y1+x2-y2)

Thus profit = sales - purchase costs - storage costs

= 10x1+9x2 - 10y1-9y2 - 10*(100+x1-y1) - 10*(100+x1-y1+x2-y2)

= -10x1-x2+10y1+y2-2000

Thus the objective function (Z) = -10x1-x2+10y1+y2-2000. This has to be maximized.

c. Constraints:

(i) 100+x1-y1<=600 (ending inventory at the end of week 1 cannot exceed 600)

(ii) 100+x1-y1+x2-y2<=600 (ending inventory at the end of week 2 cannot exceed 600)

(iii)100+x1-y1+x2-y2>=200 (at least 200 pounds of shrimp must be in storage at the end of week 2)

(iv) 100+x1-y1>=0 (ending inventory at the end of week 1 cannot be negative)

(v) 100+x1-y1+x2-y2>=0 (ending inventory at the end of week 2 cannot be negative)

(vi) x1,x2,y1,y2>=0 (non negativity)

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