Ican 2021 Performance Management Question 5

A national boutique chain sells a wide range of high quality customised fashion goods. One particular outfit is bought at ₦8,000 and sold at ₦13,000. Mean holding costs per season per outfit work out at ₦500 and it costs ₦80,000 to order and receive goods in stock. The manufacturers require orders in advance and once a batch has been made it is not possible to place a repeat order. Further, it is not possible for delivery to be staggered over the fashion season. When a customer buys an outfit that requires adjustments, any alterations or adjustments are made and she collects the outfit a day or so later. Generally, if an outfit is out of stock at one boutique it can be readily obtained from another branch, usually in a matter of hours. However, if the chain as a whole runs out of an item, then not only is the profit not earned, but the ₦2,000 or so profit that comes from the extras that customers buy is also lost. If the chain has excess purchase for a season then it is expected that the chain will be able to dispose of the surplus outfits at ₦5,000 each. The pattern of past sales of a comparable outfit show the following probability distribution for the chain as a whole: | Outfits sold | Probability | |--------------|-------------| | 1,100 | 0.30 | | 1,200 | 0.40 | | 1,300 | 0.20 | | 1,400 | 0.10 | The problem facing the management accountant of the chain is to decide how many outfits to order for the season ahead, in order to maximise expected profit, bearing in mind the penalties for over and under ordering.