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Please answer the following questions with step-by-step details and equations. Highlight the final solution for each questions A Chemical Shop in Toronto needs to purchase

Please answer the following questions with step-by-step details and equations. Highlight the final solution for each questions

A Chemical Shop in Toronto needs to purchase a special raw material from its vendor. The annual demand is 12960 units. The purchase price of each unit is $12. The ordering cost is $500. per time and it is fixed. The vendor is located in BC, so the shop needs to wait for 14 days for the order to arrive. The annual inventory carrying cost is $1 per unit. (Round off answers to the nearest whole number)

Answer Q1- Q5

Assume that the shop manager uses the continuous review inventory system and the shop operates 360 days during the year with constant daily usage.

Q1. What is the optimal order quantity?

Q2. How many numbers of order to place every year?

Q3 What is the average inventory?

Q4 When the Chemical Shop should place the order?

Q5 What is the total inventory cost, including total order cost, total holding cost, and total purchase cost?

Answer Q6 to Q9

Due to the production adjustment, the daily usage of such special raw materials is no longer constant. Assume that the daily usage now follows a normal distribution with a mean of 36 units and a variance of 16 units squared. The shop Manager wants to keep the shortage probability to no more than 4%.

Q6 What is the service level this shop wants to maintain?

Q7 What is the optimal order quantity?

Q8 What is the safety stock level?

Q9 Does the reorder point change? If so, what is the new reorder point now?

Answer Q10 to Q12

Due to a system failure, the Chemical Shop cannot maintain a continuous monitoring of its inventory, and thus, the shop now has to check its inventory every 30 days. During a recent inventory check onOct. 30th, the shop manager finds the current inventory is 120 units. The daily usage still follows a normal distribution with a mean of 36 units and a variance of 16 units Squared.

Q10 When should the shop make the order?

Q11 To maintain the shortage probability to no more than 4% what should be the order size?

Q`12 If the shop manager wants to maintain a service level of 97.5%, will the safety stock increase or decrease? What should be the order size?

Note: Below are information for service level and corresponding Z scores.

Service level = 96%, Z-score=1.75

Service level= 97.5%, Z-score=1.96

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