Galaxy Co. sells virtual reality (VR) goggles, particularly targeting 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. (a) What is the average monthly profit resulting from its policy of stocking 140 pairs of goggles 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 140 and 160 pairs of goggles. 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 dollar. The average difference between the net profit generated by a replenishment level of 160 versus a replenishment level of 140 is $ . It means, that monthly replenishment level of maximizes profitability.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Galaxy Co. sells virtual reality (VR) goggles, particularly targeting 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.

(a)	What is the average monthly profit resulting from its policy of stocking 140 pairs of goggles 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 140 and 160 pairs of goggles. 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 dollar.
	The average difference between the net profit generated by a replenishment level of 160 versus a replenishment level of 140 is $ . It means, that monthly replenishment level of maximizes profitability.