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There is a hospital Centre. The centre purchased two laundry products, including softeners and detergents from suppliers. The price of each product is $400 per pack, which is the purchase cost per unit of the centre. The annual demand for softener and detergent is 20,000 and 40,000 packs respectively. Every time an order is placed, there will be a fixed cost of $180, which is the common cost of detergent and softener. Specific product ordering costs for softeners and detergents are US$125 and US$70 per order, respectively. The annual cost of each pack of detergent and softener remains the same at 5% of the purchase cost of each pack. Meets the assumptions of the Economic Order Quantity (EOQ) model. Please note that the fixed cost of each order includes ordinary order and product-specific order costs, and these costs should be considered when calculating EOQ.

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(a)

(a1) If detergent and softener are ordered and delivered jointly, determine the ordering cost per order, optimal number of orders per year, optimal order quantity for detergent, optimal order quantity for softener, and the total annual cost (i.e., the sum of annual purchase, ordering and holdingcosts).

(a2) In order to encourage the center to buy more detergent per order, the supplier now offers a discount for the entire unit quantity. If the purchase lot size is 2,000 packs or more, a 2% discount is provided for each pack price. The holding cost of each pack of detergent is 5% of the purchase cost of each pack. Detergent will not be purchased together with softener in a lot in this case.

If the Center orders detergent independently and does not want the discount offer, determine the EOQ based on the regular price, the order quantity and the total annual cost (i.e., the sum of annual purchase, ordering and holding costs) for purchasing detergent.

(a3) If the Center orders detergent independently and wants to accept the discount offer, determine the EOQ based on the discounted price, the order quantity and the total annual cost (i.e., the sum of annual purchase, ordering and holding costs) for purchasing detergent.

(a4) From a logistics managers point of view, discuss THREE factors that the Center should consider for the adoption of the order quantity with the discount offer.