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.

(a) What is the average monthly profit resulting from its policy of stocking 100 routers at the beginning of each month? Round your answer to the nearest whole number. $

(b) What is the proportion of months in which demand is completely satisfied? Round your answer to the nearest whole number. %

(c) Use the simulation model to compare the profitability of monthly replenishment levels of 100, 120, and 140 routers. Which monthly replenishment level maximizes profitability?

Use the corresponding 95% confidence intervals on the average profit to make your comparison. Round your answers to the nearest whole number.

Lower Bound: $

Upper Bound: $