please finish part a to e, thank you.

Question 3. Sourcing decisions in a Supply Chain [45 points] Consider a retailer selling a single perishable (newsvendor type) product. The demand for the product is random and follows a Normal distribution with mean 2000 and standard deviation 500, i.e., Normal (2000, 5009). The per-unit retail price is $260. Any leftover inventory at the end of selling season is salvaged (e.g. selling in a secondary market at a discount) by the retailer with per unit value $60. Any unsatisfied demand is lost and for each unsatisfied demand, the retailer incurs an additional $10 good-will cost (e.g., the retailer needs to provide consumers a $10 voucher as compensation, etc). The retailer procures the products from his supplier, and the per-unit manufacturing cost incurred by the supplier to produce the product is $80. (a) Suppose the retailer orders from the supplier under a wholesale price contract and the supplier charges per unit wholesale price $120. What is the retailer's optimal order quantity? (b) What is the supplier's expected profits under the wholesale price contract in part (a)? (c) What is the retailer's expected profits under the wholesale price contract in part (a)? (d) Who is bearing the demand risk (i.e., suffer from the demand uncertainty) under the wholesale price contract in part(a) the retailer, the supplier, or both? (e) Suppose the supplier and the retailer agree to use a revenue sharing contract with per unit wholesale price $w and the retailer shares 40% of the retail revenue $260 with the supplier and the retailer keeps the remaining 60%. However, the per-unit salvage value $60 from selling the leftover inventories at the secondary market is not shared with the supplier, and hence the retailer gets to keep the entire $60. For what value of w such that the decentralized supply chain is coordinated (i.e., the first-best solution can be achieved)