QUESTION 1

(a) Four special cases and difficulties arise at times when using graphical approach to solving LP problems. Briefly outline these cases

(b) House Appliances Ltd produces two models of commercial toaster, the ‘Standard' and the ‘Deluxe'. Components of the toasters are processed by two different machines A and B. To complete one unit of the ‘Standard' model requires 1 hr of machine A and 1 hr of model B; likewise, one unit of the ‘Deluxe' model requires 2 hrs of machine A and 5 hrs of machine B. During a week there are only 20 hrs of machine A time available and 35 hrs of machine B time available. The company can sell all units produced and the profit on each unit sold is $10 for ‘Standard' model and $ 30 for the ‘Deluxe' model. The company wishes to maximize its weekly profit

(a) Formulate the above in terms of a Linear Programming problem

(b) Solve this linear program graphically. Determine the quantity of each type of toaster that will maximise the maximum profit

QUESTION 2

(a) Briefly describe the requirements for an effective inventory management

(b) Identify and discuss the different types of costs that are involved in an inventory system

(c) Carpet World Ltd in London stocks carpet in its biggest warehouse and sells it through its different sales point throughout the United Kingdom. The store keeps several brands and styles of carpet in stock; however its biggest seller is the Cashmeri carpet. The company has estimated an annual demand of 10 000 m2 of this type of carpet. The annual carrying cost per meter of carpet is £0.75 and the ordering cost is £150

(i) Determine the optimal order size and total inventory cost for this brand of carpet

(ii) The store would like to know the number of orders that will be made annually. Assume that the daily demand for Cashmeri carpet stocked in the warehouse is normally distributed with an average daily demand of 30 m2 and a standard deviation of 5 m2 per day. The lead time for receiving a new carpet order is 10 days. The store is open everyday except Sunday, Thanksgiving day and Christmas day

(iii) Determine the reorder point and safety stock if the store wants a service level of 95% with a probability of stockout of 5%

QUESTION 3

Genesis Computers Ltd supplies microcomputers to universities and colleges in Mauritius. It despatches them from its three assembly units located at Port Louis, Rose Belle and Flacq.
The firm is able to supply the following numbers of microcomputers to four academic institutions, which have made orders that must be delivered and installed by January 2009. The transportation costs (in Rs) per microcomputer from each distribution point are given in the table below

(a) Use Least Cost Method to determine the minimum transportation costs

(b) Use the Stepping Stone Method to determine the optimal transportation costs