Answered: Problem #4 – The mean number of air…

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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Question

Problem #4 – The mean number of air conditioning units assembled per month by Freeze, Inc. is 750 and the standard deviation is
100 units.

A) If the number of air conditioning units assembled per month follows a normal distribution, calculate the probability
of Freeze, Inc. to assemble a quantity of air conditioning units greater than the monthly break-even point calculated in problem
3-a.

Problem #3 – At Freeze Inc. the manufacturing of each air conditioning has a variable cost of $400 per unit and it takes place in a
facility that has a monthly fixed cost of $200,000.
a. If Freeze Inc. sells each unit at $1,200 how many units do they need to sell every month to break-even?

B) An improved assembling process is proposed to Freeze, Inc. to reduce the variable cost from $500 per unit to $400 per unit., increase the mean number of air conditioning units assembled per month from 750 to 850 and reduce the standard deviation to 90 units. As a result of the improvements, monthly fixed costs would go up from $250,000 to $300,000. Once these improvements are implemented, calculate the new number of air conditioning units that Freeze Inc. must sell every month to break-even, discuss and justify if you would recommend the process improvement initiative.

C) If the number of air conditioning units assembled per month still follows a normal distribution after the
implementation of the improvements described on item (b), calculate the probability of Freeze, Inc. to assemble a quantity of air conditioning units greater than the new monthly break-even point. Now that you know this probability, would you change your recommendation? Justify.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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