Use management LINEAR PROGRAMMING SIMPLEX METHOD

Ensure the "objective function" is used and graphed.

Question 1 (60 marks) The Sharma Factory in Fiji produces shirts and trousers for an Australian fashion retailer. The factory makes a profit of $ 7.00 on each shirt and $ 10.00 on each pair of trousers. The production process for both shirts and trousers involves two departments - the cutting department and the sewing department. The cutting department has a capacity of 12,000 people-hours for next month; the sewing department has a capacity of 10,000 people-hours next month. Each shirt requires 0.20 people hours of cutting and 0.25 people-hours of sewing; each pair of trousers required 0.40 people-hours of cutting and 0.10 hours of sewing. The factory has sufficient stocks of cotton fabric to produce up to 50,000 shirts per month and enough polyester fabric to make up to 20,000 pairs of trousers per month. The factory is committed to produce 15,000 shirts and 10,000 pairs of trousers next month to comply with the conditions of its contract with the Australian retailer. The factory also has an obligation to the Government of Fiji to use at least 14,000 people-hours of labour each month in order to retain its low tax status. (a) How many shirts and trousers should be produced in the next month to honour commitments and maximise profit? What is the maximum profit? You use a graphical method and calculate the exact solution values. (40 marks) Briefly outline the effect on Sharma's production mix and profit if the following situations were to arise. Each situation should be considered independently. (b) For some reason, only the guaranteed minimum labour usage of 14,000 people hours can be used? (10 marks) (c) The Australian retailer reduces its requirement for trousers to 8,500 for the next month. (5 marks) (d) As a result of a fire, 75 per cent of the cotton fabric 'is destroyed and can't be replaced for next month's production