The daily demand for a spare engine part is a random variable whose distribution,$$based on past experience, is given below:$$Number of demands per day Probability$00\mathrm{.}2110\mathrm{.}3820\mathrm{.}1930\mathrm{.}1440\mathrm{.}08$The parts cost $$1500$ each and $$5000$ each when purchased on an emergency basis. Unused parts$$can be scrapped for $10\%$ of their purchase price.$$Part A$.$ How many parts should be acquired to maximize expected profit?$$Note: Even though the setting described here is not exactly the standard newsvendor problem$$with revenue and salvage value, the same concept of underage $($shortage$)$ and overage $($excess$)$costs apply; you just need to derive these costs with the parameters described in this problem.$$Part B$.$ Now suppose the planning horizon is over $400$ days with only one purchase opportunity$$in advance of the $400$ day period and the daily demand following the same distribution as before.$$Assume demands from one day to the next are independent. The part is expected to be obsolete$$after $400$ days with the same salvage value as in part A$.$ Other cost parameters are the same as in$$Part A as well. Furthermore, holding costs for unused parts are