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In mainland China, a Chinese herbal medication called Lianhua Qingwen (LH) capsule is often used to speed up the recovery of COVID-19 symptoms. A drug store in Hong Kong wishes to buy LH capsules from a drug factory in Hebei Province, North China, and sell them to Hong Kong customers. The following information is from a two-stage make-to-order (MTO) supply chain.

Two stages

• Seller: Chinese drug manufacturer produces and sells the LH capsules to the Hong Kong drug store

• Buyer: Hong Kong drug store is a retailer who faces customer demand

Retailer information

• Wholesale price paid by retailer to manufacturer is $55 per pack

• Sale price of LH capsules is $120 per pack

• Salvage value is $0 (unsold LH capsules cannot be resold to third parties)

• Purchase lot size is 500 packs

Manufacturer information

• Production lot size is 500 packs

• Salvage value is $0 (unsold LH capsules cannot be resold to third parties)

• Fixed production cost is $5,000

• Variable production cost is $20 per packs

When answering the following questions, show the units and processes of calculation.

Question:

1(a) Determine the Hong Kong drug stores expected profit if the order quantity is 3,000 packs and determine the optimal order quantity that will maximize the drug stores profit.

1(b) If the Hong Kong drug store adopts the optimal order quantity of Q1(a), determine the drug manufacturers profit.

The drug store has forecasted the product demand (see the table below). Demand (packs) Probability (%) 2,000 25 2,500 30 3,000 45 The drug store has determined the expected profits for different order quantities (see the table below). Expected profit 130,000 Demand (packs) Probability (%) Order quantity (packs) Profit ($) Order quantity (packs) Profit ($) Order quantity (packs) Profit ($) 2,000 25 2,000 130,000 2,500 102,500 3,000 ? 2,500 30 2,000 130,000 2,500 162,500 3,000 ? 3,000 45 2,000 130,000 2,500 162,500 3,000 ? 147,500