Tablet Co makes two types of tablet computer, the Xeno (X) and the Yong (Y). X currently generates a contribution of $30 per unit and Y generates a contribution of $40 per unit. There are three main stages of production: the build stage, the program stage and the test stage. Each of these stages requires the use of skilled labour which, due to a huge increase in demand for tablet computers over recent months, is now in short supply. The following information is available for the two products:
Tablet Co is now preparing its detailed production plans for the next quarter. During this period it expects that the skilled labour available will be 30,000 hours (1,800,000 minutes) for the build stage, 28,000 hours (1,680,000 minutes) for the program stage and 12,000 hours (720,000 minutes) for the test stage. The maximum demand for X and Y over the three-month period is expected to be 85,000 units and 66,000 units respectively. Fixed costs are $650,000 per month.
Due to rapid technological change, the company holds no inventory of finished goods.
Required:
(a) On the graph paper provided, use linear programming to calculate the optimum number of each product which Tablet Co should make in the next quarter assuming it wishes to maximise contribution. Calculate the total profit for the quarter. (14 marks)
(b) Calculate the amount of any slack resources arising as a result of the optimum production plan and explain the implications of these amounts for decision-making within Tablet Co. (6 marks)