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PROBLEM 1 (10 points) A manufacturer of cement produces ordinary Portland cement and low heat Portland cement in a rotary kiln. The production rates, profits, requirements for calcareous material and rotary Kiln space are tabulated below for each type of cement. The available amount of calcareous material per month for both products is 1,400 tons, and the capacity of the rotary Kiln is 6 000 m3 The products are manufactured 4 month per year the rest of the time being allocated to the production of other types of cement The ordinary and low heat Portland cements thus share total available calcareous material and rotary Kiln space Ordinary Portland Low Heat Portland Cement Cement Production rate (tons per month) 200 100 Profit ($ per ton of cement) 1.800 3.200 Calcareous material (tons per month) 240 Rotary Kiln space (m2 per ton of cement) 300 400 160 Formulate an LP model to maximize profit Let XA denote the tons of ordinary Portland cement