Windhoek Limited produces two products, product W and product L. These products are processed in three departments: Department P, Department Q and Department R. The selling prices and machining costs per unit in each department are as follows: Product W Product L Selling price N$84 N$128 Machining costs: Dept. P N$40 N$30 Dept. Q N$16 N$60 Dept. R N$24 N$30 The machining costs per hour to produce each unit of Product W are as follows: Dept. P N$5/hour Page 13 of 15 Dept. Q - N$4/hour and; Dept. R - N$2/hour. To produce one unit of Product L, the machining costs per hour are as follows: Dept. P- N$3/hour Dept. Q N$6/hour and; Dept. R N$5/hour. Due to the age of the machines in Windhoek Limited, it is anticipated that there will be only 11 000 machine hours available in Dept. P, 9 000 hours in Dept. Q and 12 000 hours in Dept. R for the forth-coming period. Windhoek Limited are not sure how many units of each product can they produce given this resource constraint they are currently facing. Requirement Marks 3.1 Using the graphical method of linear programming, determine the optimal number of units to be produced on each of the two products in order to maximise profits for the forth-coming period. 15 3.2 Calculate the value of any slack (if any) emanating from your recommended production mix in (2.1) above). 6 3.3 Explain how Windhoek Limited can make use of shadow prices, quoting specific issues from this question and using appropriate calculations where relevant. 4 3.4 The management of Windhoek Limited is of the opinion that the optimum solution can be more accurate if the simplex method is applied. Prepare the extended model that can be used to solve this problem if the simplex method is used. 10 3.5 Explain under what situations is the graphical method more appropriate and under what situations the simplex method is more appropriate. 2 Total 37

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