3. For a four-level supply chain presented in figure 1, a raw material supplier sells the raw material at a wholesale price wS per unit to the manufacturer. Now, the manufacturer produces the product and sells it to the distributor at a wholesale price wM per unit. Now, the distributor completes the packaging activities of the product and sells it to the retailer at a wholesale price wD per unit. Now, the retailer sells the product at a retail price p per unit. The retailer experiences a demand of its product characterized by a deterministic and price dependent demand function q=(1p), where the market size and price sensitiveness of the customer is assumed as 1. Also, it is assumed that all the supply chain members incur negligible per unit production or packaging cost, i.e., zero. Here, S,M,D,R represents the profit of the raw material supplier, manufacturer, distributor, and retailer, respectively. Based on this information, answer the following questions. Figure 1. Mechanism in a four-level supply chain a) Determine the optimal value of wS, i.e., wholesale price set by the raw material supplier. [1] b) Determine the optimal value of wM, i.e., wholesale price set by the manufacturer. [1] c) Determine the optimal value of wD, i.e., wholesale price set by the distributor. [1] d) Determine the optimal value of p, i.e., retail price set by the retailer. [1] e) Determine the optimal value of S, i.e., profit of the raw material supplier [1.5] f) Determine the optimal value of M, i.e., profit of the manufacturer [1.5] g) Determine the optimal value of D, i.e., profit of the distributor [1.5] h) Determine the optimal value of R, i.e., profit of the retailer [1.5]