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Quiz Number 1

Quiz Number 1. Group 1 – North of Newark Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave Neal Deyanira Pena Professor Kenneth D. Lawerence New Jersey Inst. Of Tech. Problems Assigned . Ragsdale 2.13, 2.16, 2.20 3.10, 3.13, 3.16, 3.21, 3.24, 3.28, 3.41, 3.44, 3.45 Dielman

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Quiz Number 1

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  1. Quiz Number 1 Group 1 – North of Newark Thamer AbuDiak Reynald Benoit Jose Lopez Rosele Lynn Dave Neal Deyanira Pena Professor Kenneth D. Lawerence New Jersey Inst. Of Tech

  2. Problems Assigned • Ragsdale • 2.13, 2.16, 2.20 • 3.10, 3.13, 3.16, 3.21, 3.24, 3.28, 3.41, 3.44, 3.45 • Dielman • 3.6 • 3.24

  3. Ragsdale 2.13 by Reynald The marketing manager for Mountain Mist soda needs to decide how many TV spots and magazine ads to run during the next quarter.

  4. Initial Set up • Decision Variable • The number of TV spots and magazine ads to run • X1 = TV Spot • X2 = Magazine Ad • Objective function • TV spots expected to increase sales by 300,000 cans • Magazine ads expected to increase sales by 500,000 cans • Mountain Mist makes .05 cents a can • MAX: 0.05 * (300,000X1 + 500,000X2 ) • Constraints • A total of $100,000 may be spent • No more than $70,000 may be spent on TV spots • No more than $50,000 may be spent on magazine ads • 5,000X1 + 2,000X2 <= 100,000 • 5,000X1 <= 70,000 • 2,000X1 <= 50,000

  5. Excel Initial Settings • D7 = (B7*B6+C7*C6)*C15 • D10 = B10*B6 + C10*C6 • D11 = B11*B6 + C11*C6 • D12 = B12*B6 + C12*C6 • Changing Cells B6 and C6

  6. Solver

  7. Results • In order to maximize profit Mountain Mist should run 10 TV spots and 25 Magazine ads which will result in $775,000 in profit.

  8. Ragsdale 2.16 by Rosele • Problem: What combination of generators and alternators should Electrotech Corporation manufacture in order to maximize profit? • Decision variables: how many generators and alternators should the Electrotech Corporation manufacture? • X1 = generator X2 =alternator • Objective Function: How can the Electrotech Corporation get the • maximum income? • MAX: 250 X1 +150 X2

  9. Constraints Each generator requires 2 hours of wiring, each alternator requires 3 hours of wiring. Electrotech can not exceed a total of 260 hours wiring time. 2 X1 +3 X2< 260 • Each generator requires 1 hour of testing time, each alternator requires 2 hours of testing time. Electrothech can not exceed a total of 140 hours testing time. 1X1 +2X2<140 • Electrotech decides it needs to make at least 20 generators and 20 alternators. X1>20 X2>20

  10. LP Model MAX: 250 X1 +150 X2 Subject to: 2 X1 +3 X2< 260 1X1 +2X2<140 X1>20 X2>20

  11. Solver Parameters

  12. Electrotech Corporation Generators Alternators Number to Make 100 20 Total Profit Unit Profits 250 150 $28,000 Constraints Used Available Wiring Hrs Required 2 3 260 260 Testing Hrs Required 1 2 140 140

  13. Summary If additional wiring time becomes available at a reasonable cost should Electrotech do so? Why or why not? No, Electrotech should not do so because they do not see an increased profit since they are again only making 120 units.

  14. Electrotech Corporation Generators Alternators Number to Make 100 20 Total Profit Unit Profits 245 145 $27,400 Constraints Used Available Wiring Hrs Required 2 3 260 500 Testing Hrs Required 1 2 140 140

  15. Problem 2-20, Thamer AbuDiak • Decision Variables: • X1: Number of hours that Mine1 worked • X2: Number of hours that Mine2 worked • Objective functions: • MIN: 200X1+160X2 • Constrains: • 6X1+2X2 >= 12 • 2X1+2X2 >= 8 • 4X1+8X2 >= 24 • X1 >=0 • X2 >=0 • Answer: • 1 Hour of Operation/Day for Mine 1 • 3 Hour of Operation/Day for Mine 2 • Before • After

  16. Problem 2-20 cont., Thamer AbuDiak

  17. Ragsdale 3.10 by Deyanira A. LP Model x1= contemporary tables x2= country tables MAX: 450x1 + 350x2 } revenue Subject to: 2.0x1 + 1.5x2 1000 } router constraint 4.5x1 + 3.0x2  2000 } sander constraint 1.5x1 + 2.5x2  1500 } polisher constraint X1  .30 } has to produce at least 30% X2  .20 } has to produce at least 20% X1  0 ) simple lower bound 1X2  0 } simple lower bound

  18. Spread Sheet Furniture Manufacture   Contemporary Country     Number of Makes     Total Revenue   Unit Revenue $450 $350 $0   Constraints     Used Available Router 2 1.5 0 1000 Sander 4.5 3 0 2000 Polisher 1.5 2.5 0 1500 

  19. Microsoft Excel 11.0 Answer Report • Worksheet: [quiz 1 problems 10-13 Ch 3.xls] Sheet1 • Target Cell (Max) • Cell Name Original Value Final Value • $D$6 Unit Revenue Total Revenue $ 227,777.78 $ 227,777.78 • Adjustable Cells • Cell Name Original Value Final Value • $B$5 Number of Makes Contemporary 74.07407407 74.07407407 • $C$5 Number of Makes Country 555.5555556 555.5555556 • Constraints • Cell Name Cell Value Formula Status Slack • $D$9 Router Used 981.4814815 $D$9<=$E$9 Not Binding 18.51851852 • $D$10 Sander Used 2000 $D$10<=$E$10 Binding 0 • $D$11 Polisher Used 1500 $D$11<=$E$11 Binding 0 • $B$5 Number of Makes Contemporary 74.07407407 $B$5>=0.3 Not Binding 73.77407407 • $B$5 Number of Makes Contemporary 74.07407407 $B$5>=0 Not Binding 73.77407407 • $C$5 Number of Makes Country 555.5555556 $C$5>=0 Not Binding 555.3555556 • $C$5 Number of Makes Country 555.5555556 $C$5>=0.2 Not Binding 555.3555556

  20. Optimal Solution Furniture Manufacture   Contemporary Country     Number of Makes 74.07407407 555.5555556 Total Revenue   Unit Revenue $450 $350 $227,777.78   Constraints     Used Available Router 2 1.5 981.481 1000 Sander 4.5 3 2000 2000 Polisher 1.5 2.5 1500 1500

  21. Lp model. x1= bonds x2= home mortgages x3= car loans x4= personal loans Max: .10x1 + .085 x2 + .095x3 + .125x4 } total return Subject to: x4  162500 } 25% of total portfolio x2  x4 } invest more on mortgages than personal loans x1  x4 } invest more on bond than personal loans x1 + x2 + x3 + x4 = $650,000 } total investment x1,x2,x3,x4  0 } no negativity conditions Ragsdale 3.13 by Deyanira

  22. Spreadsheet Bank Portfolio Amount Invested Maximum Return • Bonds $0 0 10% • Home Mortgages $0 0 8.5% • Car Loans $0 0 9.5% • Personal Loans $0 $162,500.00 12.5% • Total $ 0 • Total Investment: $ 0 • Total Available: $ 650,000.00

  23. Microsoft Excel 11.0 Limits Report • Worksheet: [quiz 1 problems 10-13 ch 3.xls]Sheet2 • Target • Cell Name Value • $D$9 Total Return $ 66,625.00 • Adjustable Lower Target Upper Target • Cell Name Value Limit Result Limit Result • $B$5 Bonds Amount Invested $325,000.00 $325,000.00 $66,625.00 $325,000.00 $66,625.00 • $B$6 Home Mortgages Amount Invested $162,500.00 $162,500.00 $66,625.00 $162,500.00 $66,625.00 • $B$7 Car Loans Amount Invested $ - $ - $66,625.00 $ - $66,625.00 • $B$8 Personal Loans Amount Invested $162,500.00 $162,500.00 $66,625.00 $162,500.00 $66,625.00

  24. Excel 11.0 Answer Report • Worksheet: [quiz 1 problems 13 ch 3.xls]Sheet2 • Target Cell (Max) • Cell Name Original Value Final Value • $D$9 Total Return $ 66,625.00 $ 66,625.00 • Adjustable Cells • Cell Name Original Value Final Value • $B$5 Bonds Amount Invested $ 325,000.00 $ 325,000.00 • $B$6 Home Mortgages Amount Invested $ 162,500.00 $ 162,500.00 • $B$7 Car Loans Amount Invested $ - $ - • $B$8 Personal Loans Amount Invested $ 162,500.00 $ 162,500.00 • Constraints • Cell Name Cell Value Formula Status Slack • $B$11 Total Investment: Amount Invested $ 650,000.00 $B$11=$B$12 Binding 0 • $B$5 Bonds Amount Invested $ 325,000.00 $B$5>=$B$8 Not Binding $162,500.00 • $B$6 Home Mortgages Amount Invested $ 162,500.00 $B$6>=$B$8 Binding $ - • $C$5 Bonds Maximum 0 $C$5>=$C$5 Binding 0 • $C$6 Home Mortgages Maximum 0 $C$6>=$C$6 Binding 0 • $C$7 Car Loans Maximum 0 $C$7>=$C$7 Binding 0 • $B$5 Bonds Amount Invested $ 325,000.00 $B$5>=0 Not Binding $325,000.00 • $B$6 Home Mortgages Amount Invested $ 162,500.00 $B$6>=0 Not Binding $162,500.00 • $B$7 Car Loans Amount Invested $ - $B$7>=0 Binding $ - • $B$8 Personal Loans Amount Invested $ 162,500.00 $B$8>=0 Not Binding $162,500.00 • $B$8 Personal Loans Amount Invested $ 162,500.00 $B$8<=$C$8 Binding 0

  25. Optimal Solution Bank Portfolio Amount Invested Maximum Return • Bonds $325,000.00 0 10% • Home Mortgages $162,500.00 0 8.5% • Car Loans $ 0 9.5% • Personal Loans $162,500.00 $162,500.00 12.5% • Total $ 66,625.00 • Total Investment: $ 650,000.00 • Total Available: $ 650,000.00

  26. Ragsdale 3.16 by Jose Decision Variables M1 = Number of electric trimmers to make M2 = Number of buy trimmers to make B1 = Number of electric trimmers to buy B2 = Number of gas trimmers to buy Objective Function MIN: 55M1 + 85M2 + 67B1 + 95B2 Constraints Subject To: M1 + B1 = 30,000 M2 + B2 = 15,000 0.2M1 + 0.4M2  10,000 0.3M1 + 0.5M2  15,000 0.1M1 + 0.1M2  5,000 M1, M2, B1, B2  0 Solved by Jose F. Lopez

  27. Ragsdale 3.16

  28. The Solver Solved by Jose F. Lopez

  29. Ragsdale 2.21 by Jose Decision Variables X1 = Number of workers starting at 12 am X2 = Number of workers starting at 4 am X3 = Number of workers starting at 8 am X4 = Number of workers starting at 12 pm X5 = Number of workers starting at 4 pm X6 = Number of workers starting at 8 pm Objective Function MIN: X1 + X2 + X3 + X4 + X5 + X6 Constraints Subject To: X6 + X1  90 X1 + X2  215 X2 + X3  250 X3 + X4  165 X4 + X5  300 X5 + X6  125 Xi  0 Solved by Jose F. Lopez

  30. Solution Solved by Jose F. Lopez

  31. The Solver Solved by Jose F. Lopez

  32. Ragsdale 2.24 by Rosele • 3-24 • Problem: How many of each type of apartment should the developer produce while leasing 5 one bedroom apartments and 8 two bedroom apartments to a silent partner, having a maximum of 40 units per location, and 40,000 square feet per location?

  33. Decision variables: how many of each type of apartment should the developer produce? X1 = efficiencies X2 = one bedroom apartments X3 = two bedroom apartments X4 = three bedroom apartments Objective Function: How can the developer get the maximum income? MAX: 350 X1 +450 X2 +550 X3 +750 X4

  34. Constraints: The developer can build no more than 15 one bedroom apartments, 22 two bedroom apartment and 10 three bedroom apartments. As well, the silent partner requires the developer to lease to him 5 one bedroom apartments and 8 two bedroom apartments. Upper and Lower Bounds: X1>0 X2>5and< 15 X3>8 and < 22 X4< 10 Each efficiency requires 500 square feet, each one bedroom apartment requires 700 square feet each two bedroom apartment requires 800 square feet and each three bedroom apartment requires 1000 square feet. The developer can not exceed a total of 40,000 square feet in a location. 500 X1 +700 X2 +800 X3 +1,000 X4< 40,000 Zoning restrictions only allow 40 or less units per location X1 +5X2 + 8X3 + X4<40

  35. LP Model MAX: 350 X1 +450 X2 +550 X3 +750 X4 Subject to: X1>0 X2>5 and < 15 X3>8 and < 22 X4< 10 500 X1 +700 X2 +800 X3 +1,000 X4< 40,000 X1 +5X2 + 8X3 + X4<40

  36. Solver Parameters

  37. Real Estate Development Project Efficiencies 1 Bedroom 2 Bedroom 3 Bedroom Number to Make 0 8 22 10 Total Profit Units to Rent $350 $450 $550 $750 $23,200 Constraints Used Available Sq. Ft Reqd. 500 700 800 1,000 33,200 40,000 Units Required 1 1 1 1 40 40

  38. Questions C and D C. The optimal solution is to make: no – efficiencies 8 – one bedroom apartments 22 – two bedroom apartments 10- three bedroom apartments D. The number of units to make limits the builders potential income. In this example the builder maxed out at 40 units while only using 33,200 square feet.

  39. Problem 3-28, Thamer AbuDiak

  40. Decision Variables: • X11: Newspaper to be used for Newsprint, X12: Newspaper to be used for Packaging. • X21: Mixed Paper to be used for Newsprint, X22: Mixed Paper to be used for Packaging, X23: Mixed Paper to be used for Print Stock. • X31: White Office Paper to be used for Newsprint, X32: White Office Paper to be used for Packaging, X33: White Office Paper to be used for Print Stock. • X41: Cardboard to be used for Newsprint, X42: Cardboard to be used for Packaging. • Objective functions: • MIN (6.5+15)/.85 X11 + (11+15)/.80 X12 + (9.75+16)/.90 X21 + (12.25+16)/.90 X22 + (9.5+16)/.70 X23 + (4.75+19)/.90 X31 + (7.75+19)/.85 X32+ (8.5+19)/.80 X33+ (7.5+17)/.80 X41+ (8.5+17)/.70 X42 • Simplifying: 25.29 X11 + 32.5 X12 + 28.61 X21 + 31.39 X22 + 36.43 X23 + 26.39 X31 + 31.47 X32+ 34.38 X33+ 30.63 X41+ 36.43 X42 • Constrains: • X11 + X21 + X31 = 500, Newsprint that the company needs to produce. • X12 + X22 + X32 + X42 = 600, Packaging that the company needs to produce. • X13 + X23 + X33 = 300, Print Stock that the company needs to produce. • X11/.85 + X12/.80 <= 600, Maximum Newspaper available. • X21/.90 + X22/.80 + X23/.70 <= 500, Maximum Mixed Paper available. • X31/.90 + X32/.85 + X33/.80 <= 300, Maximum White Office Paper to available. • X41/.80 + X42/.70 <= 400, Maximum Cardboard available. • X11, X12, X21, X22, X23, X31, X32, X33, X41, X42 >= 0, Non Negativity Constrain. • Before • After • Answer BOX: (After Recycling): Newsprint produced from Newspaper: 499 Packaging produced from Newspaper: 10 Newsprint produced from Mixed Paper: 1 Packaging produced from Mixed Paper: 56 Print Stock produced from Mixed Paper: 300 Newsprint: produced from White Office Paper: 0 Packaging produced from White Office Paper: 255 Print Stock produced from White Office Paper : 0 Newsprint produced from Mixed Paper: 0 Packaging produced from Mixed Paper: 279

  41. Ragsdale 3.41 by Dave Eagle's Beach Wear and Gift Shop GOAL: Minimize Net Financing Costs Jan Feb March April May June Accounts Receivable 1.50 1.00 1.40 2.30 2.00 1.00 Planned Payments 1.80 1.60 2.20 1.20 0.80 1.20 Beginning Cash Balance = $400,000? Desired Monthly Balance >=$25,000? Finance OptionAvailable for monthLoan termFinance Charge A) Delay Pymt 1,2,3,4,5,6 1 month 2.0% B) Borrow 75% A/R 1,2,3,4,5,6 1 month 1.5% C) Short Term Loan 1 6 months 1.0% / month Defining the Decision Variables A1, A2, A3, A4, A5, A6 = amount (in $1,000s) financed in option A at the beginning of months 1,2,3,4,5,6, respectively. B1, B2, B3, B4, B5, B6 = amount (in $1,000s) financed in option B at the beginning of months 1,2,3,4,5,6, respectively. C1 = amount (in $1,000s) financed in option C at the beginning of month 1.

  42. 3.41 cont. • monthly balance = (total amount available @ beginning of month) - (payment) + A/R + (amount financed) • Interest = 0.5% per month

  43. Ragsdale 3.44

  44. Ragsdale 3.45

  45. Dielman 3.6 by Reynald Standard error = 1.84975; R-Sq = 5.7%; R-Sq(adj) = 3.4% • The same regression equation relating dividends to EPS • DIV = 0.3740EPS + 2.0336

  46. Cont. b) Is there a linear relationship between dividend yield and EPS? • Hypothesis: Ho: B1 = 0, H1: B1 ~= 0 • Decision Rule: Reject H0 if t > 2.021 or t < -2.021, Do Not Reject if -2.021 <= t <= 2.021 • Test: t = 1.56 • Decision: Do not reject c) There is not sufficient evidence to conclude that a linear relationship between dividend yield and EPS d) Construct a 95% confidence interval estimate of B1 • 0.374 +- ( 2.021 )( 0.2395 ) • 0.374 +- 0.4840 e) Construct a 95% confidence interval estimate of B1 • 2.0336 +- ( 2.021 )( 0.5405 ) • 2.0336 +- 1.0924

  47. Dielman 3.24 by Dave Dave Neal / Group North Dielman Problem 3.24 • (Dependent Variable): Y = COST is the total cost of the production run. • (Independent Variable): X = NUMBER is the number of items produced during that run. • Regression calculated using Minitab. • Regression Analysis: COST versus NUMBER • The regression equation is COST = 28.3 + 2.15 NUMBER

  48. b. What percentage of the variation in “Y” has been explained by the regression? R-Sq = regression sum of squares(SSR)/total sum of squares(SST) = 1813.9/1991.3 = 91.1% Predictor Coef SE Coef T P Constant 28.311 4.083 6.93 0.000 NUMBER 2.1549 0.1437 15.00 0.000 S = 2.84016 R-Sq = 91.1% R-Sq(adj) = 90.7% Analysis of Variance Source DF SSMS F P Regression 1 1813.91813.9 224.86 0.000 Residual Error 22 177.5 8.1 Total 23 1991.3

  49. c.Are “Y” and “X” linearly related? Conduct a hypothesis test to answer this question and use a 5% level of significance. • Hypothesis to be tested: Is the “total cost of a production run” linearly related to the “number of items produced during that run”? • The hypotheses are: H0:1 = 0 (Cost does not change when number of items produced increases) Ha:1 ≠ 0 (Cost does change) • The decision rule: If the data fits well, Mean Square Regression (MSR) will be large compared to the Mean Square due to Error (MSE). Reject H0 if t > 2.074 or if t < -2.074 • The test statistic: F statistic = (MSR) / (MSE). • Decision: F statistic = 1813.9 / 8.1 = 223.9 The MSR is large relative to the MSE. T = 15.00 > 2.074 (reject H0). • Conclusion: There is a significant relationship between project size and cost.

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