A steel company has two mills. Mill I costs $70,000 per day to operate, and it...

 

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A steel company has two mills. Mill I costs $70,000 per day to operate, and it can produce 400 tons of high-grade steel,500 tons of medium-grade steel, and 450 tons of low-grade steel each day. Mill 2 costs $60,000 per day to operate, and it can produce 350 tons of high-grade steel, 600 tons of medium-grade steel, and 400 tons of low-grade steel each day. The company has orders totaling 100,000 tons of high-grade steel, 150,000 tons of medium-grade steel, and 125,000 tons of low-grade steel. How many days should the company run each mill to minimize its costs and still fill the orders? 1). (10) Please set up the LP model for the above situation. 2). (20') Solve this model graphically, and tell how many days should we run Mill 1 (M1) and how many days should we run Mill 2 (M2) at optimal? 3). (10¹) Whether we have slack or surplus variable applicable in this question? If we do, what is the value of slack (or/and surplus) variable? What is the meaning behind it? 4). (10) What is the cost at the optimal solution? A steel company has two mills. Mill I costs $70,000 per day to operate, and it can produce 400 tons of high-grade steel,500 tons of medium-grade steel, and 450 tons of low-grade steel each day. Mill 2 costs $60,000 per day to operate, and it can produce 350 tons of high-grade steel, 600 tons of medium-grade steel, and 400 tons of low-grade steel each day. The company has orders totaling 100,000 tons of high-grade steel, 150,000 tons of medium-grade steel, and 125,000 tons of low-grade steel. How many days should the company run each mill to minimize its costs and still fill the orders? 1). (10) Please set up the LP model for the above situation. 2). (20') Solve this model graphically, and tell how many days should we run Mill 1 (M1) and how many days should we run Mill 2 (M2) at optimal? 3). (10¹) Whether we have slack or surplus variable applicable in this question? If we do, what is the value of slack (or/and surplus) variable? What is the meaning behind it? 4). (10) What is the cost at the optimal solution?

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1 LP Model Let M1 Number of days Mill 1 is operated Let M2 Number of days Mill 2 is operated Objecti... View the full answer