A factory works 8 hours a day, producing three products namely A, B and C. each of these products is processed in three different operations namely 1, 2 and 3. The processing times in minutes for each of these products in each of the operations are given below along with utilization of the processes and the cost and price in kwachas for each of these three products which have unlimited demand.     Product Processing time (mins) in operation Cost/unit Price/unit             (K) (K)       1 2 3                     A 4 3 1 10 16     B 2 1 4 8 12     C 3 4 5 5 10                 Utilisation 80% 70% 90%                     i. Formulate a linear programming model for this problem.   ii. Determine the optimal product mix using the simplex method.     Give the interpretations for the values obtained in the final simplex table

Use the following information for the next 3 problems: ABC Company plans to construct a 60,000 sq. ft private warehouse and rent public warehouse as needed. Warehouse inventory turns at the rate of 2 times per month. One pound of merchandise occupies 0.2 cubic feet of warehouse space and can be stacked 10 feet high. Given aisles, and normal operating efficiency, only 50 percent of the total warehouse space is actually used for storage. Assume the facility is being built to size so no additional space is allowed for future product growth.       A private warehouse can be constructed for $36 per sq. ft. and can be amortized over 20 years. Annual fixed costs amount to $20 per sq. ft. of total space. The cost of operation is $0.03 per pound of throughput. Space may also be rented for a storage charge on inventory of $0.06 per pound per month and a handling charge of $0.05 per pound of throughput. Monthly demands for a typical year are as follows: Month Demand (lb) Jan 2,000,000…

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Deforrest Marine Motors manufactures engines for the speedboat racing circuit. As part of their annual planning cycle, they forecasted demand for the next four quarters. The number of available days of production and the anticipated demand are given below. Employees Production Rate Production Cost Backorder Cost Overtime Cost Overtime Limit Demand Q1 2,400 6,019,000 They also estimated many of the costs required to conduct operations planning. Some of these key figures are listed below. 30 70 units/employee/quarter Q2 2,200 $1,000/unit $200/unit/quarter $1,500/unit <= 25% of Reg. Production Q3 1,700 Q4 1,800 Hire Cost Fire Cost Subcontracting Cost Subcontracting Limit Inventory Cost Initial Inventory $1,200/employee $800/employee $1,800/unit 400 units maximum $100/unit/quarter 280 units Deforrest Marine Motors wishes to maintain the current number of employees for the entire year to follow a level strategy balanced with inventory and backorders as needed. What is the total cost of this…