The Copperfield Mining company operates 2 mines, which produce 3 types of ore: necromancy, legerdemain, and prestidigitation. The company has a contract to supply a smelting company with 120 tonnes of necromancy, 80 tonnes of legerdemain, and 240 tonnes of prestidigitation. Each mine produces a certain amount of each type of ore each hour it is in operation. The company has developed the following table showing how many hours it takes to mine one tonnes of ore at a given mine. Mine 1 Mine 2 Cost per hour $20000 $16000 Number of Hours of to mine one tonne Contracted Minimum (tonnes) necromancy 6 hours/tonne 2 hours/tonne 120 legerdemain 2 2 80 prestidigitation 4 12 240 Copperfield Mining wants to determine the number of hours to operate each mine so that obligations can be met at the lowest cost. a. Formulate algebraically a linear programming model for this problem (6 marks) b. Solve this problem using Excel (6 marks) c. The smelting company is interested in purchasing more necromancy. Given the constraints you face, are you able to supply more necromancy? Briefly explain why or why not. (4marks
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