Question $4.$ Solve the following inventory problem using the simulation approach.

A supermarket sells a specific mobile brand and earns a revenue of AED $490$ per mobile. An

unsold mobile incurs a holding cost of AED$40$ at the end of the month. Holding cost includes a

portion of the rent, insurance, and others. If there is any shortage, the market assigns a goodwill

cost of AED$50$ a mobile. The store has a stocking policy of $205$ mobiles a month. The demand

follows a normal distribution with a mean of $215$ and a standard deviation of $50.$

Using the given random numbers and other parameters, simulate the operation for $14$ months

and provide your simulation output below. $($Also$,$ upload your Excel file to Blackboard for

the given random numbers, not the one where you used goal seek$)$

What is the net profit of the supermarket? $($average monthly profit$)$

What is the standard deviation $($sample$)$ of the profit?

What is the service level?

Is the service level acceptable to the supermarket? If yes$/$no$,$ explain why. Why not?

To achieve a service level of $90\%,$ how many mobiles does the company stock every month? $($Hints: use goal$-$seek$).$

If the supermarket aims for an average monthly profit of $100,000,$ what price should the supermarket charge per mobile to achieve this profit?

What do you conclude about the status of the supermarket? What recommendations do you provide to improve the supermarket's performance?