North Group/Quiz 3 Thamer AbuDiak Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave Neal Deyanira Pena Professor Lawrence MIS 680

Table of Content Ragsdale Book  Deyanira Pena, 7-8, 8-22  Rosele Lynn, 7-13, 8-12  Jose Lopez, 7-19, 8-4 Dielman's book Dielman's book  Dave Neal, 6-2  Thamer AbuDiak, 7-2.  Reynald Benoit, 8-1

Ragsdale 7-8 by Deyanira Pena Min: Q Subject to: 12x1 + 4x2 >= 48 } High-grade coal required 4x1 + 4x2 >= 28 } Medium-grade coal required 10x1 + 20x 2 >= } Low-grade coal required W1((40x1+32x2)-244)/244) <= Q } goal 1 MINIMAX constraint W2((800x1+1250x2-6950)/6950)<= Q } goal 2 MINIMAX constraint W3((.20x1+.45x2-2)/2) <= Q } goal 3 MINIMAX constraint X1x2 >= 0 } nonegativity conditions W1,w2,w3 are positive constraints

Ragsdale 7-8 by Deyanira Pena

Ragsdale 7-13 by Rosele Lynn Problem: Which combination of three types of coal should be used in order to maintain the EPA’s requirements for sulfur and coal dust levels? Decision variables: Which combination of coal should be used? X1= coal type 1 X2= coal type 2 X3= coal type 3

Objective Functions: MAX: 24,000X1 + 36,000X2 + 28,000X3 } maximize steam produced MIN: 1,100X1 + 3,500X2 + 1,300X3 } minimize sulfur emissions MIN: 1.7X X X3 } minimize coal dust emissions Constraints: X1 + X2 > 0 } non-negativity constraint X1+ X2 + X3/3 < 2,500 } for each ton of coal burned less than 2,500 ppm sulfur X1+ X2 + X3/3 < 2.8 } for each ton of coal burned less than 2.8 kg coal dust Ragsdale 7-13 by Rosele Lynn

Ragsdale 7-19 by Jose F. Lopez (A & B) OBJECTIVES Maximize: 11X1 + 8X X3 + 10X4 + 9X5 Average Yield on Funds Minimize: 8X1 + 1X2 + 7X3 + 6X4 + 2X5 Weighted Average Maturity Minimize: 5X1 + 2X2 + 1X3 + 5X4 + 3X5 Weighted Average Risk CONTRAINTS Subject to: 11X1 >= 0 10X4 >= 0 8X2 >= 0 9X5 >= 0 8.5X3 >= 0 11X1+8X2+8.5X3+10X4…. +9X5 = 1

Minimize: C16 By Changing: B5:B9, C16 Subject To: C14: D14 <= C16 B10 = 1 B5:B9 >= 0 Ragsdale 7-19 by Jose F. Lopez (A & B) Ragsdale 7-19 by Jose F. Lopez (A & B)

Minimize: C16 By Changing: B5:B9, C16 Subject To: C14: D14 <= C16 B10 = 1 B5:B9 >= 0 Ragsdale 7-19 by Jose F. Lopez (A & B)

Ragsdale 8-12 by Rosele Lynn Problem: How does Thom Pearman increase his life insurance coverage while keeping $6,000 in case of emergency? How does Pearman get the minimum amount of money to invest in order to have his after tax earnings cover his planned premium payments?

Ragsdale 8-12 by Rosele Lynn Ragsdale 8-12 by Rosele Lynn Spreadsheet before Solver

Ragsdale 8-12 by Rosele Lynn Ragsdale 8-12 by Rosele Lynn Solve for Annual Return

Ragsdale 8-12 by Rosele Lynn Ragsdale 8-12 by Rosele Lynn Minimum Investment with 15% Annual Rate

b. Solver tells us that this is a non linear model. Ragsdale 8-12 by Rosele Lynn

Ragsdale 8-22 by Deyanira Pena X1= location of new plant with respect to the x-axis Y1=location of new plant with respect to the y-axis Min:  (9-x1)^2 + (45-y1)^2) +  (2-x1)^2 + (28-y1)^2 +  (51-x1)^2 + (36-y1)^2 +  (19-X1)^2 + (4-Y1)^2 Subject to:  (9-x1)^2 + (45-y1)^2 } Dalton distance constraint  (9-x1)^2 + (45-y1)^2 } Dalton distance constraint  (2-x1)^2 + (28-y1)^2 }Rome distance constraint  (51-x1)^2 + (36-y1)^2 }Canton distance constraint  (19-X1)^2 + (4-Y1)^2}Kennesaw distance constraint  (19-X1)^2 + (4-Y1)^2}Kennesaw distance constraint

Minimize: C16 By Changing: B5:B9, C16 Subject To: C14: D14 <= C16 B10 = 1 B5:B9 >= 0 Ragsdale 8-22 by Deyanira Pena

Rugger Corporation Coordinates xyDistanceMaximum Plant to Plant to PlantAllowed Dalton Rome Canton Kennesaw Total

Dielman 6-2 Dave Neal RESEARCH AND DEVELOPMENT A company is interested in the relationship between profit (PROFIT) on a number of projects and 2 explanatory variables. These variables are the expenditure on research and development (RD) and a measure of risk assigned at the outset of the project (RISK). PROFIT is measured in thousands of dollars and RD is measured in hundreds of dollars.

Dielman 6-2 Dave Neal RESEARCH AND DEVELOPMENT (cont.) 1.Using any of the given outputs, does the linearity assumption appear to be violated? Justify your answer.  PROFIT vs. RD appears to be linear. R 2 is 95.6%.  PROFIT vs. RD and RISK appears to be linear. R 2 is 99.2%.  PROFIT vs. RISK appears to violate the linearity assumption. R 2 is only 50.6%. 2.If you answered yes, state how the violation might be corrected.  PROFIT vs. RISK can be corrected by trying a quadratic and cubic polynomial regression analysis to see if the R 2 value is improved. 3.Then try your correction using a computer regression routine.  See the attached quadratic and cubic polynomial regression analysis data and plots. 4.Does your model appear to be an improvement over the original model? Justify your answer.  Yes, the quadratic and cubic polynomial regression analysis appears to be an improvement over the original model. R 2 improved from 50.6% to 71.0% within a 95% Confidence Interval.

Dielman 6-2 Dave Neal RESEARCH AND DEVELOPMENT (cont.) Regression Analysis: PROFIT versus RD The regression equation is PROFIT = RD Predictor Coef SE Coef T P Constant RD S = R-Sq = 95.6% R-Sq(adj) = 95.3% Analysis of Variance Source DF SS MS F P Regression Residual Error Total ____________________________________________________________ Regression Analysis: PROFIT versus RISK The regression equation is PROFIT = RISK Predictor Coef SE Coef T P Constant RISK S = R-Sq = 50.6% R-Sq(adj) = 47.5% Analysis of Variance Source DF SS MS F P Regression Residual Error Total

Dielman 6-2 Dave Neal RESEARCH AND DEVELOPMENT (cont.) Regression Analysis: PROFIT versus RD, RISK The regression equation is PROFIT = RD RISK Predictor Coef SE Coef T P Constant RD RISK S = R-Sq = 99.2% R-Sq(adj) = 99.0% Analysis of Variance Source DF SS MS F P Regression Residual Error Total Source DF Seq SS RD RISK Unusual Observations Obs RD PROFIT Fit SE Fit Residual St Resid R R R denotes an observation with a large standardized residual.

Dielman 6-2 Dave Neal RESEARCH AND DEVELOPMENT (cont.)

Dielman 7-2 Thamer AbuDiak Graduation Rate  Variables:  y: Percentage of students who earned a bachelor degree in 4 years (GRADRATE4)  x 1 : Admission Rate expressed as a percentage (ADMINRATE)  x 2 : indicator variable coded as 1 for private and 0 for public school.  The regression equation is:  y = x x 2

Dielman 7-2 Thamer AbuDiak Graduation Rate a.F-test: i.F = (SSE R – SSE F )/(K-L)MSE F = ( ) / (2*.0195) = ii.Decision rule: i.H0 if F > 3.49 ii.Do not reject H0 if F <= 3.49 iii.Since 86 > 3.49, the null hypotheses is rejected. b.There are difference in the graduation rate between public and private schools.

Dielman 7-2 Thamer AbuDiak Graduation Rate c.Difference in graduation rates between public and private schools. Public school: y = x 1Public school: y = x 1 Private school y = x 1Private school y = x 1 Private schools have a higher graduation rate than public schools.Private schools have a higher graduation rate than public schools.

Dielman 7-2 Thamer AbuDiak Graduation Rate Sample graduation rate prediction d.

Dielman 7-2 Thamer AbuDiak Graduation Rate Regression without counting x2 as a factor Regression with counting x2 as a factor

S R-Sq R-Sq(adj) Mallows C-p StepConstant PaperT-valueP-value MachineT-valueP-value OverheadT-valueP-value LaborT-valueP-value Dielman 8-1 Reynald Benoit Backward elimination. Alpha-to-Remove: 0.1 Response is COST on 4 predictors, with N = 27

Dielman 8-1 Reynald Benoit -cont  A) What is the equation?  COST = PAPER MACHINE  B) What is the R2?  99.87%  C) What is the Adjusted R2?  99.86%  D) What is the standard error?  11.0  E) What variables were omitted? Are they related to cost?  Overhead and Labor. They are related to cost but paper and machine explains 99% of the variation in cost.