The Lam Company's production manager is planning a series of one-month production periods for stainless steel sinks. The forecasted demand for the next four months is listed below:

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

This Lam 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 with regular production, the production manager has three other choices:

(1) He can produce up to 30 more sinks per month in overtime but at a cost of $130 per sink;

(2) He 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 can fill the demand from his 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. Backorders are NOT permitted (e.g. orders taken in period 3 to satisfy the demand for period 2 are not permitted). Inventory on hand at the beginning of month 1 is 30 sinks (i.e. beginning inventory in month 1 is 30 sinks)

Question #1: Set up and formulate algebraically the above production scheduling problem as a TRANSPORTATION Model to minimize cost.

Question #2: Solve using Excels solver (Provide the corresponding Excel Spreadsheet + Answer Report). Also, include a managerial statement that verbally describes the results.

Question #3: Does this problem have an alternate optimal solution? Justify your answer.