This is supply chain problem

Best Technology (BT) is a leading manufacturer of adhesives used in a variety of industrial applications. BT produces two types of industrial adhesives in its Texas plant for the US market. The two types of adhesives are produced using the same production technology and equipment. They have identical characteristics except their adhesive strengths which are determined by the last production step of mixing with different chemicals. The demands for the two types of adhesives are independent and their weekly demands in the US distribution centre (DC) are approximately normally distributed with their means and standard deviations given below. Adhesives Mean (kg) Standard Deviation (kg) Type I Adhesive 10,000 9,000 Type II Adhesive 4,000 3,000 The replenishment lead time of the adhesives from BT's manufacturing plant to the US DC is 4 weeks. The current adhesive production cost is $100/kg, the cost of shipping the adhesive from the plant to the DC is $20,000, and the annual holding cost rate is 50%. BT has decided to use a (Q,R) level policy to control the inventory at the DC to achieve its target service of less than 5% stock-out probability. (c) As the two types of adhesives have recently been classified as dangerous goods, they have to be shipped from the plant to the US DC in specialized chemical tank containers of size of 20,000 kg. Each tank container can store only one type of adhesive and the shipment size for each adhesive type is at most 20,000 kg. To reduce the inventory cost, BT's logistics manager has proposed to carry out the last production step at the DC instead of at the plant. According to the manager's proposal, the work-in-process inventory is shipped from the plant using a specialized chemical tank container and the time required for the last production step at the DC is negligible. Assume that carrying out the last production step at the DC will increase the production cost of the adhesives from $100/kg to $101/kg. i) Determine the annual inventory cost of the two types of adhesives kept in the DC for the case of carrying out the last production step at the Texas plant. (5 marks) ii) Determine whether BT should relocate the last production step to the DC. (5 marks) iii) Suppose that the actual annual holding cost rate, I, is unknown, and BT's estimated annual holding cost rate is equal to axI where a is a non-negative real number. Find the percentage increase in total inventory cost if BT's order quantity is much bigger than the amount of safety stock. (8 marks)