How many cases of each kind should be purchased weekly so that the needed amounts of manganese, chromium and molybdenum are obtained at the smallest possible cost? What is the smallest possible cost ?Formulate and solve by linear programming.
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3. In order to produce 1000 tons of non-oxidizing steel for engine valves, at least the following units of manganese, chromium and molybdenum, will be needed weekly: 10 units of manganese, 12 units of chromium, and 14 units of molybdenum (1. unit is 10 pounds). These metals are obtainable from dealers in nonferrous metals, who, to attract markets make them available in cases of three sizes, S, M and L. One S case costs $9 and contains 2 units of manganese, 2 units of chromium and 1 unit of molybdenum. One M case costs $12 and contains 2 units of manganese, 3 units of chromium, and 1 unit of molybdenum. One L case costs $15 and contains 1 unit of manganese, 1 unit of chromium and 5 units of molybdenum. How many cases of each kind should be purchased weekly so that the needed amounts of manganese, chromium and molybdenum are obtained at the smallest possible cost? What is the smallest possible cost ?Formulate and solve by linear programming.
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