$($All answers were generated using $1,000$ trials and native Excel functionality.$)$

Galaxy Co$.$ sells virtual reality $($VR$)$ goggles targeted to customers who like to play video games. Galaxy procures each pair of goggles for $$150$ from its supplier and sells each pair of goggles for $$300.$ Monthly demand for the VR goggles is a normal random variable with a mean of $160$ units and a standard deviation of $40$ units. At the beginning of each month, Galaxy orders enough goggles from its supplier to bring the inventory level up to $140$ goggles. If the monthly demand is less than $140,$ Galaxy pays $$20$ per pair of goggles that remains in inventory at the end of the month. If the monthly demand exceeds $140,$ Galaxy sells only the $140$ pairs of goggles in stock. Galaxy assigns a shortage cost of $$40$ 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.

The data has been collected in the Microsoft Excel file below. Download the spreadsheet and perform the required analysis to answer the questions below. Generate trials on a new worksheet.

Download spreadsheet galaxy$-$d$15$b$12,$xlsx

a$.$ What is the average monthly profit resulting from its policy of stocking $140$ routers at the beginning of each month? Round your answer to the nearest dollar.

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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 $105,140,$ and $175$ 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 dollar.

Lower Bound: $

Upper Bound: $