A manufacturer of consumer retail merchandize Mango Republic (MR) faces a problem of satisfying a fluctuating demand for one of its products. For the next four weeks, the demand for the product is estimated to be Week 1 2 3 4 Estimated Demand 3500 4100 4200 3500 During the same period of time, MR can manufacture up to 5000 units of product per week in week 1 and 2, and up to 4000 units per week in weeks 3 and 4. The demand for the product in each week must be satisfied using the sum production in that week and the inventory from a previous week - backlogs are not allowed. In the beginning of week 1 MR has no inventory in stock. The production and inventory costs for next 4 weeks are shown below. Week 1 2 3 4 Production cost ($/unit) 50 50 80 70 Inventory cost ($/unit) 10 10 10 10 MR's warehouse can store at most 800 units of product inventory in each week. MR needs to determine the production-inventory plan for the next four weeks to minimize the sum of production and inventory costs over this time period. In setting up the corresponding linear model