Question 1 25 Marks Brunswick LTD is a company that purchase toys from abroad for resale to retail stores. The company is concerned about its inventory management operation. It is considering adopting an inventory management system based upon the EOQ model. The companys estimates of its inventory management costs are shown below:

Percentage of purchase cost of toys per year Storage costs -3% Insurance- 1% Handling- 1% Obsolescence - 3% Opportunity costs of funds invested inventory 10 Fixed costs associated with placing each order for inventory are N$311.54. The purchase price of the toys to Brunswick LTD is N$4.50 per unit. There is a two-week delay between the time that new inventory is ordered from suppliers and the time that it arrives. The toys are sold by Brunswick at a unit price of N$6.30. The variable cost to Brunswick of selling the toys is N$0.30 per unity. Demand from Brunswicks customers for the toys average 10 000 units per week, but recently this has varied from 6 000 to 14 000 unit per week on the. On the basis of recent evidence, the probability of unit sales in any two week period has been estimated as follows:

Sales (Units)	Probability
12 000	0.05
16 000	0.20
20 000	0.50
24 000	0.20
28 000	0.05

If adequate inventory is not available when demanded by Brunswicks customers in any two week period, approximately 25% of order that cannot be satisfied in that period will be lost, and approximately 75% of customers will be willing to wait until new inventory arrives.

Required:

(a) Ignoring taxation, calculate the optimum order level of inventory over a one year planning period using the EOQ model. EOQ = Where: O is the fixed cost per order D is the annual sales H is the cost of carrying a unit of inventory per period expressed as a percentage of its purchase cost multiplied by the purchase price per unit of inventory. (5 Marks) (b) Estimate the level of safety inventory that should be carried by Brunswick Ltd. (8 Marks) (c) If Brunswick Ltd were to be offered a quantity discount by its suppliers of 1% for order of 30 000 units or more, evaluate whether it would be beneficial for the company to take advantage of the quantity discount. Assume for this calculation that no safety inventory is carried. (6 Marks) (d) Estimate the expected total annual cost of inventory management if the EOQ had been (i) 50 % higher, and (ii) 50% lower than its actual lever. Comment upon the sensitivity of total annual costs to changes in the economic order quantity. Assume for this calculation that no safety inventory is carried. (6 Marks)