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:

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. (1) he can produce up to 50 more sinks per month in overtime but at a cost of $130 per sink;

2. (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 450 sinks, at a cost of $150 each);

3. (3) Or, he can fill the demand from his on-hand inventory. The ending inventory cost is $10 per sink per month.

A constant workforce level is expected. Backorders are NOT permitted (e.g. order taken in period 3 to satisfy demand in later period 2 is not permitted). Inventory on hand at the beginning of month 1 is 40 sinks.

1. Formulate algebraically the Linear Programming (LP) model for the aboveproduction scheduling problem. (20 points)

Please help me properly formulate the production scheduling problem algebraically using linear programming. thanks

Month Demand for Stainless Steel Sinks 120 160 240 100 Month Demand for Stainless Steel Sinks 120 160 240 100