Problem points$]$: Computco Ltd sells personal computers. The demand for its computers in one month follows a normal distribution with a mean of $500$ and a standard deviation of $100.$ Each time an order is placed, a fixed cost of $$1000$ per order and a variable cost of $$1,500$ per computer are incurred. Computers are sold for $$2,800$ per unit. If Computco does not have computers in stock, then its customers will buy computers from a competitor. At the end of each month, a holding cost of $$10$ per computer is incurred, based on that month's ending inventory. Orders are placed at beginning of each month and arrive immediately. Computco wants to maximize its expected profit for a $2-$year period. Assume that $400$ computers are in stock at the beginning of month one, and a salvage value of $$1500$ for each computer left at the end of the second year.

a$)$ Suppose Computco uses an $(s,S)$ policy to replenish its inventory at the beginning of each month $($i$.$e$.,$ it places an order to raise the inventory to $S$ whenever the inventory is less than or equal to $s).$ The following four $(s,S)$ policies are under consideration: $1)s=100$ and $S=1000$; $2)s=200$ and $S=900$; $3)s=300$ and $S=1300$; $4)s=500$ and $S=1200.$ Develop a simulation model with Excel and run at least $1000$ iterations to determine the $(s,S)$ policy that maximizes Computco's expected profit over the $2-$year period. Show details in an Excel file.

$[20$ points$]$

b$)$ Consider a different $(Q,R)$ policy to replenish Computco's inventory at the beginning of each month $($i$.$e$.,$ it places an order of size $Q$ whenever the end$-$of$-$month inventory is less than or equal to $R).$ The following four $(Q,R)$ policies are under consideration: $1)Q=900$ and $R=100$; $2)Q=600$ and $R=200$; $3)Q=1,000$ and $R=300$; and $Q=1,200$ and $R=500.$ Develop a simulation model with Excel and run at least $1000$ iterations to determine which $(Q,R)$ policy maximizes Computco's expected profit over the $2-$year period. Show details in an Excel file.

$[20$points$]$