PLEASE INCLUDE ALL THE STEPS AND INSTRUCTIONS.

NB: Include any assumptions if you need them. Use two-decimal precision in your numeric values. You must show all your work/steps in your calculations to receive a full mark. Use MS Equation Editor for writing your formulae, calculations etc. If need be, use MS Excel for drawing graphs and MS PowerPoint for diagrams, and include snapshots of Excel Solver optimality results. Please write your responses directly below each question. Question \#1. [15 points out of 50] Consider a dyadic SC with one manufacturer (M) and one retailer (R), specializing in the manufacturing and sales of a differentiated product; call it ABC. The annual market demand for ABC, solely supplied by this SC, is estimated as d(p)=500,00040,000p, where p is the purchase price. It costs M$2 to manufacture one unit of ABC. a) Currently, M wholesales, and R retails ABC at a unit price 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. d) Now, 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