Problem 2 (30 points)

The J. Mehta Companys production manager is planning a series of one-month production periods for stainless steel sinks. The forecasted demand for the next four months is as follows:

Month	Demand for Stainless Steel Sinks
1	100
2	160
3	240
4	120

The Mehta firm can normally produce 100 stainless steel sinks in a month. This is done during regular production hours at a cost of $100 per sink. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices:

1. He/she can produce up to 30 more sinks per month in overtime but at a cost of $130 per sink;
2. He/she can purchase a limited number of sinks from a friendly competitor for resale (the maximum number of outside purchases over the four-month period combined is 200 sinks, at a cost of $150 each);
3. Or, he/she can fill the demand from his/her on-hand inventory (i.e. beginning inventory). The inventory carrying cost is $10 per sink per month (i.e. the cost of holding a sink in inventory at the end of the month is $10 per sink).

A constant workforce level is expected. Back orders are NOT permitted (e.g. orders taken in period 3 to satisfy the demand for period 2 is not permitted). Inventory on hand at the beginning of month 1 is 30 sinks (i.e. beginning inventory in month 1 is 30 sinks)

1. Set up and formulate algebraically the above production scheduling problem as a TRANSPORTATION Model to minimize cost. (18 points)

2. Solve using Excels solver (Provide the corresponding Excel Spreadsheet and the Answer Report). Also include a managerial statement that describes verbally the results. (10 points)

3. Does this problem have an alternate optimal solution? Justify your answer. (2 points)

Note: This problem can be formulated as a multi-period production scheduling LP problem. However, if you try to formulate it this way then you will get ZERO as the problem requirement is to formulate it as a transportation problem.