$(3$ Points$)$

Galaxy Co$.$ distributes wireless routers to Internet service providers. Galaxy procures each

router for $$75$ from its supplier and sells each router for $$125.$ Monthly demand for the

router is a normal random variable with a mean of $100$ units and a standard deviation of

$20$ units. At the beginning of each month, Galaxy orders enough routers from its supplier

to bring the inventory level up to $100$ routers. If the monthly demand is less than $100,$

Galaxy pays $$15$ per router that remains in inventory at the end of the month. If the

monthly demand exceeds $100,$ Galaxy sells only the $100$ routers in stock. Galaxy assigns a

shortage cost of $$30$ for each unit of demand that is unsatisfied to represent a loss$-$of$-$

goodwill among its customers. Management would like to use a simulation model to

analyze this situation. Perform the simulation for $1000$ times, what is the average monthly

profit resulting from its policy of stocking $100$ routers at the beginning of each month? $---$ please solve in excel