G 115 120 Question 3 (25 marks) Windhoek Enterprises manufactures two products from different combinations of the same resources. Unit selling prices and unit cost details for each product are as follows: Product D N$ per unit Ns per unit Selling price Direct material A (N$5 per kg) Direct material B (N$3 per kg) Skilled labour (N$7 per hour) Variable overhead (N$2 per machine hour) Fixed overheads 28 Profit 20 10 12 24 28 21 14 18 36 13 11 Fixed overheads are absorbed using absorption rate per machine hour. This is an unavoidable central overhead cost which is not affected by the mix or volume of product produced. The maximum weekly demand for products D and G is 400 units and 450 units respectively, and this is the normal weekly production volume achieved by Windhoek Enterprises. However, for the next four weeks the Page 11 of 16 FACULTY OF COMMERCE, MANAGEMENT AND LAW achievable production level will be reduced as a result of a shortage of available resources. The resources that are expected to be available per week are as follows: Direct material A 1800 kg Direct material B 3500 kg Skilled labour 2500 hours Machine time 6500 machine hours QTY 308.33 416.67 The following is the final simplex tableau derived from the information above. Variables in D G Skilled Machine Material A Material B solution mix labour time D 1 0 0 0 0.34 -0.08 Skilled labour 0 0 1 0 -0.86 -0.17 0 1 0 0 -0.16 0.17 Machine time 0 0 0 1 -0.89 -0.92 Z row ? ? ? ? ? ? C-Z row ? ? ? ? ? ? 283.33 1791.67 ? Marks Sub total Total 77 Required Formulate the equations for the objective function and the constraints for the 3.1 above problem? The optimal solution for this problem is shown on the simplex report above, 3.2 complete the Z row. C-Z row and interpret the results (all amounts in Qty column, Z row and C-Z row for material A as well as material B). Total 18 25 25