Question 3. (40%) Hotel GW is a famous 5-star franchise chain in a hotel business in North America and their headquarter in North Woods manages all the suppliers for their franchise hotels. The headquarter buys a special pine-scented bar soap from a soap producer. The producer has a soap production plant nearby North Woods operating 365 days per year. This soap is shipped in cases of 100 bars and the purchase price is $20 per case. Ordering cost is $200 each time and the annual holding cost for this shop is $8 per case. The demand of the soap is 50,000 cases per month from all franchise hotels. 1) What is the optimum order size that the hotel may use? (10%) 2) Calculate the total annual cost under the optimum order size. (10%) 3) If the soap plant can produce upto 4000 cases per day and delivers the daily maximum everyday to GW until all the order quantity is fulfilled, how the order size and annual total cost will change. (20%)