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Question: please show all work and do parts ad please please...

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1. The Home Depot warehouse stocks a variety of tools and other home improvement supplies that are sold at local Home Depot stores around Atlanta. One Dewalt hammer is especially popular and is purchased from the supplier for $4.50 each. The estimated order processing and receipt costs are around $125 per order. Home Depot uses a 23% annual interest rate to account for inventory carrying costs The monthly demand for the hammer follows a Normal distribution with μ = 150 and σ = 45 The lead time for orders is assumed to be 3 months. Assume that back-orders occur when there is demand for a hammer, but the warehouse has none, and the cost for back-ordering is $15 (a) What is the optimal order quantity and the reorder level? (b) Determine the annual cost of setup, holding, and stock-outs associated with the hammer assuming that the optimal policy is used (c) What is the cost of uncertainty? In other words, compare the annual cost obtained in part (b) with the average annual cost that would be incurred if the lead time demand had zero variance (d) Now suppose that the stock-out cost is replaced with a Type-1 service objective of 90 percent. Find the optimal values of (Q, R) in this case

please show all work and do parts a-d!!! please please answer this i know its long

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