2 Production Planning Consider the daily operation of a supply chain consisting of one supplier and 10 buyers, i 1,...,10. In each day, each buyer i has probability pi = 0.7 to place an order (to the supplier) with order quantity D; following a discrete uniform distribution U[1, 10]. buyers' ordering decisions are independent of each other. The supplier's unit production cost is $1K. In each day, the supplier first produces 2 = 50 units of the product, then receives all the orders from the buyers and satisfies them as much as possible. The unit selling price is $10K, and each unit of leftover costs the sup- plier $1K to dispose. Let V(2) be the supplier's expected daily profit under production quantity 2. Assume sample size N = 365. (a) What is the distribution (histogram) of the daily total order quantities received by the supplier? Graph it. (b) What is the 90% confidence interval of the expected daily profit for the supplier? (c) What is the supplier's probability of shortage? And what is the probability that the supplier has leftover? (d) What is the profit-maximizing production quantity 2* for the supplier? Graph V (x) against r to support your conclusion. (e) Buyer Collusion: To gain bargaining power, 10 buyers consolidate their procurement and re- duce the selling price to $ 7K. They coordinate their ordering process as follows: in each day, each supplier i first observes their individual demand D; ~ U[0, 10]. Then if the consolidated demand D;> 35, all orders will be placed; otherwise, no order will be placed. The supplier's opera- tion and other parameters remain the same. What is the profit-maximizing production z* for the supplier under buyer collusion