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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2CYU

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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