Question 1:
Consider the problem of operating a warehouse, by buying and selling the stock of a certain commodity, in order to maximize profit over four periods. The warehouse has a fixed capacity of 50 units of commodity. There is a cost of 30 cents per unit of commodity for holding stock for one period. The purchase price of the commodity changes over four months as $10, $12, $8 and $10. In any period the same price holds for both purchase and sale. The warehouse is originally empty and is required to be empty at the end of the last period. In all periods, there is a purchase restriction of $960.
a. Formulate the problem as an optimization problem. Clearly state the decision variables, the objective function and constraints.
b. Solve the problem using LINDO. Print out clearly your LINDO input and output.
c. Use LINDO sensitivity analysis to answer the following questions:
- What is the most that the warehouse manager should be willing to
pay to buy an additional unit of warehouse space in the last period? Justify your answer.
Question 2:
A firm has three factories in different locations. The monthly capacities of factories to produce a good are 6, 6 and 7 units, respectively. Market demand for the good in 4 various areas are 4, 5, 4 and 5 units per month. The following table gives the monthly transportation cost per unit of supplying the good from each factory to the markets:
Cost from different factories to different markets
Market 1 Market 2 Market 3 Market 4
Factory 1 2 6 6 2
Factory 2 3 3 8 5
Factory 3 2 5 3 4
a. Formulate a balanced transportation problem to minimize the shipping costs.
b. Use the Northwest Corner method to find an initial basic feasible solution to the problem.
c. Use the transportation simplex (u--v) method to find an optimal solution to the problem. Show the details of the iterations.