Question 1: Newsvendor Problem (25 points)

A retailer buys sunbeds at the beginning of each summer for the sales during summer. The demand for sunbeds is distributed uniformly between 100 and 200. The purchasing cost of each sunbed is $30, respectively. Any sunbed can be sold for $50 each. By the end of the selling season, left-over sunbeds can be returned to their suppliers for a discounted price. This discounted selling price is $20. There is also a $2 handling cost for each left-over sunbed.

a. [10 points] Compute the optimal number of sunbeds that retailer should buy at the beginning of summer?

b. [5 points] What is the probability of satisfying the entire demand?

c. [10 points] What is the number of expected shortages and expected leftovers when the optimal quantity is ordered?