a ) Explain and graphically show the following terms as used in linear programming: 1) Alternate optimal or multiple solutions ii ) Unbound solutions iii) Infeasible solutions b ) The Copper Wire Company is a manufacturer of copper wires. Ben Muturi, the company executive director has just received a memo from Stella Musingo, one of his young engineers. Stella informs Ben that; with the forthcoming purchase of new blast furnace to produce copper, it seems an opportune time to completely review their method of producing copper. Currently, a variety of ingredients are entered into the blast furnace in order to produce copper. The production manager, Joe Kiilu makes the decision, as he has for the last 25 years, on the variety of ingredients. It is not an easy decision. The company wants to keep the costs of producing copper down The ingredients into the blast furnace have to interact to produce copper. Furthermore, the chemical reactions have to be such that the copper produced is viscous enough to flow out of the furnace. Stella has identified the problems with the current method. First, Joe is retiring in six months and there is no obvious replacement to him. Second, the company never knows if they are minimizing the production costs. Third, sometimes the furnace does not freeze-up. Stella believes that there is a quantitative technique, which can be used to decide what ingredients to enter in to the furnace. Once the model has been developed, special skills such as Joe's will no longer be required. The company will also be confident that they are minimizing costs. In addition, they would be able to eliminate the furnace freeze-up problem Required: 1) What potential quantitative technique can be used to solve this problem? Why? ii ) Specify the general formulation of the quantitative technique. (Be sure to clearly spell out the meaning of all the variables or parameters used) iii) If a group were formed to develop an appropriate model, what organizational personnel should be included? What specific skills would each provide? (Q 6 June 1998)