Newsvendor Replenishment under Uncertain Demand (25 points): Answer any 25 points of questions from set IIIbelow.You are a retailer. You buy a product at $3.00 from a supplier and sell it for $5.0. It costs the supplier $2.00. Unsold items can be marked down and sold for $1.50. Demand is normally distributed between with mean 200 and standard deviation 40.

1)(10points) Newsvendor Quantity:How many units should you stock? Why?How would the quantity stocked change if demand isdiscrete uniformly distributedbetween 100 and 300.Note: Discrete uniform means that demand only takes on integer values from 100 thru 300 and that each value has an occurrence probability of 1/201. Use the discrete uniform only in answering this sub-question.

2)(10points)Newsvendor with Supplier and Retailer: How would the number of units stocked changeif you look at the quantity decision from the perspective of the supply chainconsisting of the supplier + retailer? Would the chains expected profit increase or decrease relative to the quantity choice in part 1above? Explainthe logic behind your answers.

3.) (*15 points) Probability:Consider the independent-retailer situation in part 1. A senior executive at your retail company asks the following Suppose we were to stock 220 units. What is the probability that our realizedprofitwill be at least $405? Note: You are concerned here with realized profitnot expected profit; realized profit is the profit corresponding to the actual demand value that is realized (occurs) for this item over the selling season, while expected profit averages over all possible demand values.

4)(*5 points) Relation between Expected Profit and Critical Ratio value:Let Newsvendor Expected Profit = Csx Expected Sales Cox Expected Leftover, where Sales = min(Q, Demand), Leftover = Q Sales, with Q = Newsvendor Quantity.

In the news vendor problem, the expected profit _________ as the critical ratio ____________.Pick from options belowand explain the reasoningfor your choice. a. decreases,increasesb. decreases, decreasesc. increases, stays the samed. stays the same, increasese. cannot say, because ______