Consider the following production planning problem for the next 3 months. Suppose you produce tables and chairs. The demands for the products are shown in Table 1.
Table 1 Demands

Backlogging is not allowed (L.e. demand has to be satisfied). Initially (at the beginning of month 1) you have 30 tables, 70 chairs and 15 desks in inventory initially. One table requires  units of raw material, one chair requires  units of raw material and one desk requires  units of raw material. Each month, 400 units of raw material is available. One table requires 5 hours of labor, one chair requires 4 hours of labor and one desk requires 3 hours of labor. In months 1 and 2 , 1000 hour of labor hours is available. The unit production costs are shown in Table 2.
Table 2 Unit Production costs in TL

Unit inventory cost is  table,  chair and  desk. (Inventory cost is charged for end of month inventories) You can also purchase tables and chairs from an cutside supplier at a higher cost in periods 2 and 3 only for a unit price of  and . respectively. The maximum number of tables that can be purchased is 20 for each of these months whereas this number is 30 for chairs. Formulate a linear programming model to minimize total cost for 3 months.