Molly O'Malley is the new manager of the materials storeroom for Tudor Manufacturing. Mollly has been asked to estimate future monthly purchase costs for part #696, used in two of Tudor's products. Molly has purchase cost and quantity data for the past 9 months as follows: Month Cost of Purchase Quantity Purchased January $12,410 2,650 parts February 12,770 2,850 March 17,403 4,116 April 15,838 3,761 May 13,249 2,901 June 14,022 3,376 July 15,237 3,644 August 10,087 2,287 September 14,900 3,592 Estimated monthly purchases for this part based on expected demand of the two products for the rest of the year are as follows: Month Purchase Quantity Expected October 3,350 parts November 3,770 December 3,050 The computer in Molly's office is down, and Molly has been asked to immediately provide an equation to estimate the future purchase cost for part #696. Molly grabs a calculator and uses the high-low method to estimate a cost equation. What equation does she get? Using the equation from requirement 1, calculate the future expected purchase costs for each of the last 3 months of the year. After a few hours Molly's computer is fixed. Molly uses the first 9 months of data and regression analysis to estimate the relationship between the quantity purchased and purchase costs of part #696. The regression line Mollyobtains is as follows: y = $2,505.3 + 3.54X Evaluate the regression line using the criteria of economic plausibility, goodness of fit, and significance of the independent variable. Compare the regression equation to the equation based on the high-low method. Which is a better fit? Why? Use the regression results to calculate the expected purchase costs for October, November, and December. Compare the expected purchase costs to the expected purchase costs calculated using the high-low method in requirement. Comment on your results.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Molly O'Malley is the new manager of the materials storeroom for Tudor Manufacturing. Mollly has been asked to estimate future monthly purchase costs for part #696, used in two of Tudor's products. Molly has purchase cost and quantity data for the past 9 months as follows:

Month	Cost of Purchase	Quantity Purchased
January	$12,410	2,650 parts
February	12,770	2,850
March	17,403	4,116
April	15,838	3,761
May	13,249	2,901
June	14,022	3,376
July	15,237	3,644
August	10,087	2,287
September	14,900	3,592

Estimated monthly purchases for this part based on expected demand of the two products for the rest of the year are as follows:

Month	Purchase Quantity Expected
October	3,350 parts
November	3,770
December	3,050

The computer in Molly's office is down, and Molly has been asked to immediately provide an equation to estimate the future purchase cost for part #696. Molly grabs a calculator and uses the high-low method to estimate a cost equation. What equation does she get?

Using the equation from requirement 1, calculate the future expected purchase costs for each of the last 3 months of the year.

After a few hours Molly's computer is fixed. Molly uses the first 9 months of data and regression analysis to estimate the relationship between the quantity purchased and purchase costs of part #696. The regression line Mollyobtains is as follows:

y = $2,505.3 + 3.54X

Evaluate the regression line using the criteria of economic plausibility, goodness of fit, and significance of the independent variable. Compare the regression equation to the equation based on the high-low method. Which is a better fit? Why?

Use the regression results to calculate the expected purchase costs for October, November, and December. Compare the expected purchase costs to the expected purchase costs calculated using the high-low method in requirement. Comment on your results.

Expert Answer

Expert Solution

Step 1: Evaluation of total cost function

Given data:

Month	Cost of Purchase	Quantity Purchased, X
January	12410	2,650 parts
February	12770	2850
March	17403	4116
April	15838	3761
May	13249	2901
June	14022	3376
July	15237	3644
August	10087	2287
September	14900	3592

High-low method: In above table mark the highest and lowest value in each column.

Variable cost:

$V C equals s l o p e comma space m equals fraction numerator 17403 minus 10087 over denominator 4116 minus 2287 end fraction equals bold 4$

Fixed cost:

$F C equals c o n s tan t comma space c equals y minus m x equals 17403 minus open parentheses 4 cross times 4116 close parentheses equals bold 939$

Linear equation ( slope intercept-form):

$Y equals m X plus c$

Total cost function is given by

$bold italic T bold italic o bold italic t bold italic a bold italic l bold space bold italic c bold italic o bold italic s bold italic t bold equals bold 939 bold plus bold 4 bold italic x$

Where x is the quantity of purchased.

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