Linear Programming exam-style practice question: Maxilla Ltd Maxilla Ltd makes two products: the Xebec and the Yuko. Both products use the same type of materials and the same grade of direct labour. However, Xebec and Yuko use these resources in somewhat different proportions. Standard revenues and costs per unit for the two products are shown below: Xebec Yuko f Selling price 148 122 Costs: Material A (at 10 per kg) (40) (40) Material B (at 12 per kg) (12) (24) Direct labour (at 14 per hour) (56) (28) Fixed overheads (absorbed at 7 per direct labour hour) (28) (14) Standard profit 12 16 In any week, the maximum availability of input resources is limited to the following: Material A 120 kg Material B 50 kg Direct labour 100 hours The fixed overhead absorption rate of 7 per direct labour hour is based on the assumption that the maximum amount of available direct labour hours are used each and every week. It is company policy to not hold inventory of either finished goods or raw materials Required: a) Formulate the objective function and the constraints to be used in a linear programming model that could be applied to determine the optimum weekly production plan. (Note: You are NOT required to draw or sketch a graph). (Question continues over page) Weekly production of Yukos T- 45 LABOUR 40 35 - 30 Re aska 20 1$ 10- M MATERIALA CONTRIBUTION 360o WATELALE n 1 T - S- Weekly T production 5 10 15 20 N P 35 40 45 W of Xebecs Maxilla Ltd question requirements continued: b) You may assume that the sketch shown above represents, in the form of a reasonably accurate graph, the linear programming model for determining the optimal weekly production plan. Referring to the graph, solve the relevant simultaneous equations to determine the production policy that will maximise the weekly profit of the company, and calculate the exact value of the optimal weekly profit. c) Calculate the shadow (or 'dual') price of direct labour. d) Management are considering the introduction of overtime, which would be paid at a premium of 25% above the normal wage rate. Determine whether this policy would be worthwhile and (if it is) calculate how many overtime hours should be worked each week. e) Now assume that overtime working is NOT an option. Instead, management are considering an increase in the selling price of the Yuko. Calculate the maximum selling price of Yuko at which the optimal product mix calculated in (b) above would remain optimal. 1) Discuss the limitations and potential shortcomings of the linear programming approach to tackling problems such as those faced by the company in this
