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B3- 1. Cut and Stitch (CS) make two types of suits using skilled tailors (labour) and a delicate and unique fabric (material). Both the tailors and the fabric are in short supply and so the accountant at CS has correctly produced a linear programming model to help decide the optimal production mix. The model is as follows: Variables: Let W = the number of work suits produced Let L = the number of lounge suits produced Constraints Tailors’ time: 7W + 5L ≤3,500 (hours) – this is line T on the diagram Fabric: 2W + 2L ≤1,200 (metres) – this is line F on the diagram Production of work suits: W ≤400 – this is line P on the diagram Objective is to maximise contribution subject to: C = 48W + 40L
On the diagram provided the accountant has correctly identifi ed OABCD as the feasible region and point B as the optimal point. Required: (a) Find by appropriate calculation the optimal production mix and related maximum contribution that could be earned by CS. (4 marks) (b) Calculate the shadow prices of the fabric per metre and the tailor time per hour. (6 marks) The tailors have offered to work an extra 500 hours provided that they are paid three times their normal rate of $1·50 per hour at $4·50 per hour. Required: (c) Briefl y discuss whether CS should accept the offer of overtime at three times the normal rate. (6 marks) (d) Calculate the new optimum production plan if maximum demand for W falls to 200 units. (4 marks)
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