Grecaf Co. Ltd. manufactures two industrial products: x-100, which sells for Sh.4,500 a unit, and Y-120...

  

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Grecaf Co. Ltd. manufactures two industrial products: x-100, which sells for Sh.4,500 a unit, and Y-120 which sells for Sh.4,250 a unit. Each product is processed through both of the company's manufacturing departments. The limited availability of labour, materials and equipment capacity has restricted the ability of the firm to meet the demand for its products. The production department believes that linear programming can be used to support and systematize the production schedule for the two products. The following data are available to the production department: Resources required per unit X-100 min. Direct material - weekly supply limited to 1800 Kg at Sh.600 per kilogramme Direct labour: Department 1-weekly supply limited to 10 people at 40 hours each at an hourly cost of Sh.3000 Department 2 - Weekly supply limited to 15 people at 40 hours each at an hourly rate of Sh.400 Machine time: Department I - Weekly capacity limited to 250 hours Department 2- Weekly capacity limited to 300 hours 4 Kg 40 min. Y-120 2 Kg 30 min. 1 hour 1hr.15 min 1 hour 30 0 hours The overhead costs for Grecaf Co. Ltd. are accumulated on a plant wide basis. The overhead is assigned to products on the bass of the number of direct-labour hours required to manufacture the product. This base is appropriate for overhead 1 hour assignment because most of the variable-overhead costs vary as a function of labour time. The estimated overhead cost per direct labour hour is: Sh Variable-overhead cost Fixed overhead cost Total overhead cost per direct Labour hour A = number of units of X-100 to be produced B = number of units of Y-120 to be produced 600 The production department formulated the following equations for the linear- programming (I..P) statement of the problem. Objective function to minimize costs: Minimize Z = 4250A + 3100 B Constraints: 300 300 Material: - Dept.1 labour:- Dept. 2 labour: - 4A + 2B <=1,800 Kgs. 2/3A + B <= 400 hours 1% + B<=600 hours: Non-negativity: - A => = 0, B =>0 (Note. >= is greater than or equal to and <= is less than or equal to) Required: a) Evaluate the accuracy and application of the L.P. equations prepared by the production department. marks) (6 b) Formulate and label equations for the LP. statement of the production problem in line with your findings in (a) above. (8 marks) c) Explain how L.P. could help Grecaf Co. determine how large a change in the price of direct materials would have to be to change the optimum production Mix of X-100 and Y-120 (6 marks) (Total: 20 marks) Bush manages a factory that is currently processing a large order to make hundreds of newly designed computers. Several serious production problems have been encountered. Bush is concerned whether the units will be of acceptable quality. If they are acceptable, the factory will have a net profit of Sh.1,000,000. If the units are of an unacceptable quality, the legal problems, warranty claims and unfavourable publicity will result in a net loss of Sh.625,000. However, Bush could add an intricate inspection procedure so that all defective computers could be discovered and repaired before they leave the factory. The cost of his procedure would be Sh.1,307,500 Required: a) Formulate Bush's problem as a "decision table" or "pay off table showing actions, events and outcomes. (4 marks) b) Supposes that both events are equally likely and that Bush bases his decision strictly on expected monetary return, which action will the management prefer? (6 marks) c) Suppose that Bush could obtain a consultant's special accounting analysis that would affect his assessments probabilities of acceptable or unacceptable quality. The consultant is expected to produce one of three possible reports: neutral, optimistic or pessimistic. The neutral report would not change the original decision in (b) above. The optimistic report would change Bush's assessments of probabilities to 0.7 acceptable and 0.3 unacceptable. The pessimistic report would have the reverse effect, changing the probabilities to 0.3 acceptable and 0.7 unacceptable. Bush assesses probabilities of receiving the various reports as follows: Neutral report 0.3 Optimistic report Pessimistic report What is the highest price that Bush should pay for the report? marks) 0.3 0.4 (Total: 20 marks) (10 Grecaf Co. Ltd. manufactures two industrial products: x-100, which sells for Sh.4,500 a unit, and Y-120 which sells for Sh.4,250 a unit. Each product is processed through both of the company's manufacturing departments. The limited availability of labour, materials and equipment capacity has restricted the ability of the firm to meet the demand for its products. The production department believes that linear programming can be used to support and systematize the production schedule for the two products. The following data are available to the production department: Resources required per unit X-100 min. Direct material - weekly supply limited to 1800 Kg at Sh.600 per kilogramme Direct labour: Department 1-weekly supply limited to 10 people at 40 hours each at an hourly cost of Sh.3000 Department 2 - Weekly supply limited to 15 people at 40 hours each at an hourly rate of Sh.400 Machine time: Department I - Weekly capacity limited to 250 hours Department 2- Weekly capacity limited to 300 hours 4 Kg 40 min. Y-120 2 Kg 30 min. 1 hour 1hr.15 min 1 hour 30 0 hours The overhead costs for Grecaf Co. Ltd. are accumulated on a plant wide basis. The overhead is assigned to products on the bass of the number of direct-labour hours required to manufacture the product. This base is appropriate for overhead 1 hour assignment because most of the variable-overhead costs vary as a function of labour time. The estimated overhead cost per direct labour hour is: Sh Variable-overhead cost Fixed overhead cost Total overhead cost per direct Labour hour A = number of units of X-100 to be produced B = number of units of Y-120 to be produced 600 The production department formulated the following equations for the linear- programming (I..P) statement of the problem. Objective function to minimize costs: Minimize Z = 4250A + 3100 B Constraints: 300 300 Material: - Dept.1 labour:- Dept. 2 labour: - 4A + 2B <=1,800 Kgs. 2/3A + B <= 400 hours 1% + B<=600 hours: Non-negativity: - A => = 0, B =>0 (Note. >= is greater than or equal to and <= is less than or equal to) Required: a) Evaluate the accuracy and application of the L.P. equations prepared by the production department. marks) (6 b) Formulate and label equations for the LP. statement of the production problem in line with your findings in (a) above. (8 marks) c) Explain how L.P. could help Grecaf Co. determine how large a change in the price of direct materials would have to be to change the optimum production Mix of X-100 and Y-120 (6 marks) (Total: 20 marks) Bush manages a factory that is currently processing a large order to make hundreds of newly designed computers. Several serious production problems have been encountered. Bush is concerned whether the units will be of acceptable quality. If they are acceptable, the factory will have a net profit of Sh.1,000,000. If the units are of an unacceptable quality, the legal problems, warranty claims and unfavourable publicity will result in a net loss of Sh.625,000. However, Bush could add an intricate inspection procedure so that all defective computers could be discovered and repaired before they leave the factory. The cost of his procedure would be Sh.1,307,500 Required: a) Formulate Bush's problem as a "decision table" or "pay off table showing actions, events and outcomes. (4 marks) b) Supposes that both events are equally likely and that Bush bases his decision strictly on expected monetary return, which action will the management prefer? (6 marks) c) Suppose that Bush could obtain a consultant's special accounting analysis that would affect his assessments probabilities of acceptable or unacceptable quality. The consultant is expected to produce one of three possible reports: neutral, optimistic or pessimistic. The neutral report would not change the original decision in (b) above. The optimistic report would change Bush's assessments of probabilities to 0.7 acceptable and 0.3 unacceptable. The pessimistic report would have the reverse effect, changing the probabilities to 0.3 acceptable and 0.7 unacceptable. Bush assesses probabilities of receiving the various reports as follows: Neutral report 0.3 Optimistic report Pessimistic report What is the highest price that Bush should pay for the report? marks) 0.3 0.4 (Total: 20 marks) (10

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