PLEASE SHOW WORK AND YASAI EXCEL SIMULATION VARIABLES You own a retail store that sells a product for $$129$ per unit. Every time you order a batch of the product from your supplier, it costs you a $$79$ flat fee, plus $$87$ per unit. Each day, there is $12\%$ chance of a traffic jam. On days with no traffic jam, demand has a Poisson distribution with a mean of $20\mathrm{.}8.$ On days with a traffic jam, demand is lower, having a Poisson distribution with a mean of $12\mathrm{.}1.$ On days when you have you have insufficient stock to meet demand, you only sell as many units as you have in stock, and the additional customers purchase the item from another store. If you do have enough stock to meet demand, any inventory left at the end of the day is carried over to the next day.

You make inventory replenishment decisions each morning when you open the store: if the amount S you have in stock when you open the store is at or below R units, you place an order for L $-$ S units $($enough to bring the current stock level up to L$).$ If you place an order, it is delivered the following morning, shortly before you open the store $($and is counted as part of the opening inventory for the next day$).$ You calculate your holding costs to be $$3$ per unit of ending inventory per day.

Build a YASAI simulation model for this situation, and use it to evaluate all possible combinations of R $=30,40,50,$ or $60$ and L $=50,60,70,$ or $80.$ Simulate a time period of $100$ days, with a beginning inventory of $31$ units. For all inventory left in stock or on order at the end of day $100,$ apply a "salvage" credit of $$110$ per unit.

When R $=60$ and L $=50,$ it is occasionally possible to have L $-$ S $<0$ and thus generate a negative order. When this occurs, simply use an order quantity of zero $($that is$,$ no order$).$

Questions to answer on the output sheet:

With the salvage adjustment, which policy gives the highest average profit over the $100-$day period?

Without the salvage adjustment, which policy gives the highest average profit over the $100-$day period?

For the policy maximizing expected profit with the adjustment, estimate the probability that the adjusted profit for the $100$ days will be at least $$75,000.$

Hint: the YASAI function invocation genBinomial$(1,$ p$)$ will generate a $1$ with probability p and $0$ with probability $1-$ p; this technique may be used to simulate whether or not there is a traffic jam.