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- The mean number of air conditioning units assembled per month by Freeze, Inc. is 750 and the standard 100 units. If the number of air conditioning units assembled per month follows a normal distribution, calculate the lity of Freeze, Inc. to assemble a quantity of air conditioning units greater than the monthly break-even point ed in problem 3-a. An improved assembling process is proposed to Freeze, Inc. to reduce the variable cost from $500 per 5400 per unit., increase the mean number of air conditioning units assembled per month from 750 to 850 and the standard deviation to 90 units. As a result of the improvements, monthly fixed costs would go up from ow number of air conditioning

- The mean number of air conditioning units assembled per month by Freeze, Inc. is 750 and the standard 100 units. If the number of air conditioning units assembled per month follows a normal distribution, calculate the lity of Freeze, Inc. to assemble a quantity of air conditioning units greater than the monthly break-even point ed in problem 3-a. An improved assembling process is proposed to Freeze, Inc. to reduce the variable cost from $500 per 5400 per unit., increase the mean number of air conditioning units assembled per month from 750 to 850 and the standard deviation to 90 units. As a result of the improvements, monthly fixed costs would go up from ow number of air conditioning

MATLAB: An Introduction with Applications
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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**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. 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. **Discussion Question #1** – Using your “own words”, discuss the differences among decision making under certainty, decision making under risk, and decision making under uncertainty. Provide an example for each one of them. **Discussion Question #2** – Using your “own words”, discuss how the coefficient of determination and the coefficient of correlation are related and how would you use them in regression analysis.
Transcribed Image Text:**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. 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. **Discussion Question #1** – Using your “own words”, discuss the differences among decision making under certainty, decision making under risk, and decision making under uncertainty. Provide an example for each one of them. **Discussion Question #2** – Using your “own words”, discuss how the coefficient of determination and the coefficient of correlation are related and how would you use them in regression analysis.
### Problem #3: #### Part A: - **Concept:** At the break-even point, revenue must be equal to cost. - **Details:** - We have a variable cost of $500 and a monthly fixed cost of $250,000. - This can be represented as a function: \( C(x) = 500x + 250,000 \), where \( x \) is the number of units sold. - Each unit is sold at $1,000, so the revenue function is \( R(x) = 1000x \). - **Break-even Calculation:** - At the break-even point, total revenue equals total cost: \[ 1000x = 500x + 250,000 \] - Solving the equation: \[ 500x = 250,000 \] \[ x = \frac{250,000}{500} = 500 \] - **Conclusion:** - Freeze Inc. must sell 500 units per month to meet break-even conditions.
Transcribed Image Text:### Problem #3: #### Part A: - **Concept:** At the break-even point, revenue must be equal to cost. - **Details:** - We have a variable cost of $500 and a monthly fixed cost of $250,000. - This can be represented as a function: \( C(x) = 500x + 250,000 \), where \( x \) is the number of units sold. - Each unit is sold at $1,000, so the revenue function is \( R(x) = 1000x \). - **Break-even Calculation:** - At the break-even point, total revenue equals total cost: \[ 1000x = 500x + 250,000 \] - Solving the equation: \[ 500x = 250,000 \] \[ x = \frac{250,000}{500} = 500 \] - **Conclusion:** - Freeze Inc. must sell 500 units per month to meet break-even conditions.
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