It is a common practice that suppliers provide an incentive for large order quantities by offering a lower purchase cost when items are ordered in larger quantities. In this question, we consider quantity discounts for the EOQ model. Assume that we have a product in which the basic EOQ model is applicable. Instead of a fixed unit cost, the supplier quotes the following discount schedule:

Discount category	Order size	Discount (%)	Unit cost ($)
1	0 to 999	0	5.00
2	1,000 to 2,499	3	4.85
3	2,500 and over	5	4.75

Suppose that the carrying charge is 20%, the ordering cost is $49 per order, and the annual demand is 5,000 units.

(a) Consider the EOQ model without any quantity discount (category 1). What is the EOQ? Use Excel spreadsheet to plot the (annual) total cost (holding cost plus purchasing cost) vs. the order quantity and verify that the EOQ value indeed results in the minimum total cost. What is the minimum total cost? Show the graph of the total cost function. (15 marks)

(b) Use Excel spreadsheet to plot three total cost functions (corresponding to discount categories 1 to 3) vs. the order quantity in the same graph. With the help of Excel spreadsheet and visualisation, identify the optimal order quantity that yields the minimum total cost given the above discount schedule. What is the minimum total cost? Explain your result. (15 marks)