The following is the demand for umbrellas generally faced by a retailer during the rainy season: Market Demand faced by Probability of Retailer (# of umbrellas) 300 500 800 1100 Demand 8% 11% 27% 30% 1400 14% 1700 10% The retailer places an order in advance of the rainy season to the manufacturer by paying a wholesale price of Rs. 80/unit. The umbrella sells in the market for Rs. 125/unit and any excess umbrellas have to be sold to scrap for Rs. 20/unit. The manufacturer incurs a fixed cost of production of Rs. 10,000 and his variable cost of production is Rs. 35/unit. a. What is the average demand faced by the retailer during the rainy season? (2 Marks) b. Considering that this is a make to order scenario, what is the optimal order size placed by the retailer such that his profits can be maximised? (6 Marks) C. What is the order size that maximizes profits for the entire supply chain? (4 Marks) d. Without any calculations, explore the difficulties in achieving the globally optimal solution. What contract could be explored