tice Problems

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

Galaxy Co$.$ sells virtual reality $($VR$)0$ogoles targeted to customers who like to play video games. Galaxy procures each pair of pogples for $$150$ from its supplier and sells each pair of gogoles for $$300.$ Monthly demand for the VR pogples is a normal random variable with a mean of $120$ units and a standard deviation of $30$ units. At the beginning of each month, Galaxy orders enough goggles from its supplier to bring the inventory level up to $100$ poggles. If the monthly demand is less than $100,$ Galaxy Days $$20$ per pair of goggles that remains in inventory at the end of the month. If the monthly demand exceeds $100,$ Galaxy sells only the $100$ pairs of gogoles in stock. Galaxy assigns a shortage cost of $$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.

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

$($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 $100$ and $120$ pairs of popoles. Use a $95\%$ confidence interval on the difference between the average profit that each replenishment level generates to make your comparison. Round your answer to the nearest dollat.

The average difference between the net profit oenefated by a replenlstiment fevef of $120$ versus a replenishment level of $100$ is $5-$ It means that monthly replenishment level of $$ increases profitability.