A company's distribution network has three warehouses with the same amount of demand. 1.1 This company would like to increase the total inventory in its SC by 40% to cover a risk. What is the optimal number of warehouses in the new plan? Show your work! (20 points) 1.2 Assume the weekly demand of warehouses are not equal and they are as stated in Table 1. The demand correlation matrix is in Table 2. The manager would like to know if the total inventory cost can be reduced by combining warehouse 1 and 3 if you just consider safety stock. The service level would be 90% and the lead time is 1 week for all cases. Compare two options - three separate warehouses vs. two warehouses (the new option). Which option would you choose and why? (20 points) Table 1 Weekly demand of each warehouse Warehouse Mean SD 1 100 20 2 120 15 3 200 40 Table 2 Demand correlation matrix Warehouse 1 2 3 1 1 0.2 0 2 0.2 0.5 3 0 0.5 1 A company's distribution network has three warehouses with the same amount of demand. 1.1 This company would like to increase the total inventory in its SC by 40% to cover a risk. What is the optimal number of warehouses in the new plan? Show your work! (20 points) 1.2 Assume the weekly demand of warehouses are not equal and they are as stated in Table 1. The demand correlation matrix is in Table 2. The manager would like to know if the total inventory cost can be reduced by combining warehouse 1 and 3 if you just consider safety stock. The service level would be 90% and the lead time is 1 week for all cases. Compare two options - three separate warehouses vs. two warehouses (the new option). Which option would you choose and why? (20 points) Table 1 Weekly demand of each warehouse Warehouse Mean SD 1 100 20 2 120 15 3 200 40 Table 2 Demand correlation matrix Warehouse 1 2 3 1 1 0.2 0 2 0.2 0.5 3 0 0.5 1