A company ships goods from 2 warehouses to 3 retail stores. The demands of the r

Question

A company ships goods from 2 warehouses to 3 retail stores. The demands of the retail stores are 400, 600 and 700 units respectively; whereas each warehouse has 1000 units of goods available. The per unit transportation costs are as follows: Retail Store 1 Retail Store 2 Retail Store 3 Warehouse 1 $50 $40 $75 Warehouse 2 $65 $60 The objective is to find the schedule that meets the demands of the retail stores and minimizes the total transportation cost. To formulate the problem as an LP we use the following decision variables: zij: Quantity of goods transported from warehouse i to retail store j for i 1, 2 and j 1, 2, 3. Thus a21 stands for the quantity of goods transported from warehouse 2 to retail store 1. 7. Write down the LP objective function. 8. Write down the LP constraints. 9. How does your model change if the trucks used for transportation have capacity limits? For instance, suppose at most 200 units of goods can be transported from warehouse 1 to retail store 3. Add a constraint to your model to reflect this new capacity constraint.

Explanation / Answer

7. objecttive function is to minimize Z= X11*50+X12*40+X13*75+X21*65+X22*85+X23*60 8. LP constraints X11,X12,X13,X21,X22,X23 > = 0 X11+X12+X13

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