Question C

I need solution for option C only

Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at least 18% of metal A, between 8% and 22% of metal B, no more than 9% of metal and between 30% and 65% of metal D. The proportion of the four metals in each of the six ores and cost of ores are given in the following table: Metal (9) D Cost/Ton FOUNG> 2NO OOO When the metals are processed and refined, the impurities (materials other than metals A, B, C D) are removed. The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy. a. (15 points) Formulate the problem (Define the decision variables and formulate objective function and constraints) b. (15 points) Solve the problem with Excel solver. (Label the corresponding sheet as "1"). C (20 points) Assume that there are Nores and M metals. Let P, be the percentage of metal) in ore 1,2 - 1,..., and / 1, M. Also, let be the cost of 1 ton of orelia 1...... Assume that minimum and maximum amount of metal limits are, and = 1,...M. Reformulate the problem for this general case. - a. (15 points) Formulate the problem (Define the decision variables and formulate objective function and constraints) b. (15 points) Solve the problem with Excel solver. (Label the corresponding sheet as "1 C (20 points) Assume that there are N ores and M metals. Let Py be the percentage of metal in ore 1, 1 = 1,..., N, and j = 1,..., M. Also, letc be the cost of 1 ton of ore 1,1 = 1,...,N. Assume that minimum and maximum amount of metal limits are 4 and ujj = 1, ... M. Reformulate the problem for this general case. Question 1 (50 points) Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at least 18% of metal A, between 8% and 22% of metal B, no more than 9% of metal C, and between 30% and 65% of metal D. The proportion of the four metals in each of the six ores and cost of ores are given in the following table: Ore D 0 Cost/Ton 19 23 A 26 16 22 15 0 120 Metal (%) B C 15 18 10 25 0 4 22 0 350 32 4 0 53 18 31 25 R 24 When the metals are processed and refined, the impurities (materials other than metals A, B, C, D) are removed. The company wants to know the amount of each ore to use per ton of the alloy that will minimize the cost per ton of the alloy. a. (15 points) Formulate the problem (Define the decision variables and formulate objective function and constraints) b. (15 points) Solve the problem with Excel solver. (Label the corresponding sheet as "Q1"). C. (20 points) Assume that there are N ores and M metals. Let Pij be the percentage of metalj in ore i, i = 1, ...,N, and j = 1, ..., M. Also, let cibe the cost of 1 ton of ore i, i = 1, ..., N. Assume that minimum and maximum amount of metalj limits are l; and ujj = 1, ... M. Reformulate the problem for this general case