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8. (7 pts) There are three factories located at AR, IN, and TX respectively. From these locations, a certain commodity is to be delivered to each of the two warehouses situated at A and B. The commodity can be sold for $10 per item. The weekly requirements of the warehouse are respectively 50 and 35 units of the commodity while the production capacity of the factories at AR, IN, and TX are respectively 25, 20, and 30 units. The cost of transportation per unit is given as belows. Cost Warehouse 1 Warehouse 2 AR 5 3 IN 6 6 TX 2 4 To maintain a good relationship with all the factories, warehouse 2 requires that it receives at least 40% of its product from factory in TX. Realize that it is making good profit in warehouse 1, AR requires that at least 35% of its product shipped to warehouse 1. With current shortage of supply in IN, total number of items ship from IN must be less than 50% of the whole number shipped from all factories. Formulate (without solving) a linear programming problem to maximize the profit