Consider a dyadic SC with one manufacturer (M) and one retailer (R), specializing in the manufacturing and sales of a differentiated product Y. The annual market demand for Y, solely supplied by this SC, is estimated as , where is purchase price. It costs M $2 to manufacture one unit of Y. a) Currently, M wholesales and R retails the product at the rate of $3.5, and $5.5, respectively. Calculate the profit for, M, R, and the SC. b) As in part a), assume M and R are decentralized. Determine the optimal wholesale and optimal retail price. Accordingly, calculate the profits for M, R, and the SC. Are your results for part b) better than a)? c) Suppose M and R have vertically integrated. Determine the optimal selling price and the total profit. Compared to your results in part b), calculate the percent change in total demand supplied and the percent change in total SC profit.