formulate this as a goal programming problem to help the management for the best decision and solve the problem using simplex method

QUESTION 1 a) A mining company produces two types of ore: Manganese and Copper Oxide ore. Material A is produced according to direct orders from furniture manufacturers. The Copper Oxide ore is produced according to direct orders from the concentrating plants. The Manganese ore is distributed to retail ore buyers. The average production rates for Copper Oxide ore and manganese ore are identical at 1000 metric tons per hour. By running two shifts, the operational capacity of the mine is 80 hours per week. The marketing department reports that the maximum estimated sales for the following week are 70000 metric tonnes of manganese ore and 45000 metric tonnes of copper oxide ore. According to the accounting department, the profit from a tonne of Manganese ore is USS 250, and from a tonne of Copper Oxide ore, US\$ 150. The management of the company decides that a stable employment level is the primary goal for the firm. Therefore, whenever there is demand exceeding normal production capacity, management simply expands production capacity by providing overtime. However, management feels that overtime operation of the mine of more than 10 hours per week should be avoided because of the accelerating costs. The management has the following goals, in order of importance: - The first goal is to avoid any underutilization of production capacity. - The second goal is to limit the overtime operation of the mine to 10 hours. - The third goal is to achieve the sales goals of 70000 metric tonnes and 45000 metric tonnes, respectively, for both ores. - The last goal is to minimise the overtime operation of the plant as much as possible