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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 Slide 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 Slide 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. Slide 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 + 2,000X220 Constraints Slide 10 MAX: 250 X 1 +150 X 2 Subject to: 2 X 1 +3 X 2 < 260 1X 1 +2X 2 20 X 2 >20 LP Model Slide 11 Solver Parameters Slide 12 Generators Alternators Number to Make 100 20Total Profit Unit Profits 250 150 $28,000 ConstraintsUsed Available Wiring Hrs Required 2 3 260 260 Testing Hrs Required 1 2 140 140 Electrotech Corporation Slide 13 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. Summary Slide 14 Generators Alternators Number to Make 100 20Total Profit Unit Profits 245 145 $27,400 Constraints Used Available Wiring Hrs Required2 3 260 500 Testing Hrs Required 1 2 140 140 Electrotech Corporation Slide 15 Problem 2-20, Thamer AbuDiak Decision Variables: X 1 : Number of hours that Mine1 worked X 2 : Number of hours that Mine2 worked Objective functions: MIN: 200X 1 +160X 2 Constrains: 6X 1 +2X 2 >= 12 2X 1 +2X 2 >= 8 4X 1 +8X 2 >= 24 X 1 >=0 X 2 >=0 Answer: 1 Hour of Operation/Day for Mine 1 3 Hour of Operation/Day for Mine 2 Before After Slide 16 Problem 2-20 cont., Thamer AbuDiak Slide 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 Slide 18 Spread Sheet Furniture Manufacture ContemporaryCountry Number of Makes Total Revenue Unit Revenue $450 $350 $0 Constraints UsedAvailable Router21.501000 Sander4.5302000 Polisher1.52.501500 Slide 19 Microsoft Excel 11.0 Answer Report Worksheet: [quiz 1 problems 10-13 Ch 3.xls] Sheet1 Target Cell (Max) CellName Original Value Final Value $D$6Unit Revenue Total Revenue $ 227,777.78 $ 227,777.78 Adjustable Cells CellName Original Value Final Value $B$5Number of Makes Contemporary 74.07407407 74.07407407 $C$5Number of Makes Country 555.5555556 555.5555556 Constraints CellNameCell ValueFormulaStatusSlack $D$9Router Used981.4814815$D$9=0Not Binding555.3555556 $C$5Number of Makes Country 555.5555556$C$5>=0.2Not Binding555.3555556 Slide 20 Optimal Solution Furniture Manufacture ContemporaryCountry Number of Makes 74.07407407555.5555556Total Revenue Unit Revenue $450 $350 $227,777.78 Constraints UsedAvailable Router21.5981.4811000 Sander4.5320002000 Polisher1.52.515001500 Slide 21 Ragsdale 3.13 by Deyanira A.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 Slide 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 Slide 23 Microsoft Excel 11.0 Limits Report Worksheet: [quiz 1 problems 10-13 ch 3.xls]Sheet2 Target CellNameValue $D$9Total Return $ 66,625.00 Adjustable LowerTargetUpperTarget CellName ValueLimitResultLimitResult $B$5Bonds Amount Invested $325,000.00 $325,000.00 $66,625.00 $325,000.00 $66,625.00 $B$6Home Mortgages Amount Invested $162,500.00 $162,500.00 $66,625.00 $162,500.00 $66,625.00 $B$7Car Loans Amount Invested $ - $ - $66,625.00 $ - $66,625.00 $B$8Personal Loans Amount Invested $162,500.00 $162,500.00 $66,625.00 $162,500.00 $66,625.00 Slide 24 Excel 11.0 Answer Report Worksheet: [quiz 1 problems 13 ch 3.xls]Sheet2 Target Cell (Max) CellNameOriginal ValueFinal Value $D$9Total Return $ 66,625.00 $ 66,625.00 Adjustable Cells CellName Original ValueFinal Value $B$5Bonds Amount Invested $ 325,000.00 $ 325,000.00 $B$6Home Mortgages Amount Invested $ 162,500.00 $ 162,500.00 $B$7Car Loans Amount Invested $ - $ - $B$8Personal Loans Amount Invested $ 162,500.00 $ 162,500.00 Constraints CellName Cell ValueFormulaStatusSlack $B$11Total Investment: Amount Invested $ 650,000.00 $B$11=$B$12Binding 0 $B$5Bonds Amount Invested $ 325,000.00 $B$5>=$B$8Not Binding $162,500.00 $B$6Home Mortgages Amount Invested $ 162,500.00 $B$6>=$B$8Binding $ - $C$5Bonds Maximum 0$C$5>=$C$5Binding 0 $C$6Home Mortgages Maximum 0$C$6>=$C$6Binding 0 $C$7Car Loans Maximum 0$C$7>=$C$7Binding 0 $B$5Bonds Amount Invested $ 325,000.00 $B$5>=0Not Binding $325,000.00 $B$6Home Mortgages Amount Invested $ 162,500.00 $B$6>=0Not Binding $162,500.00 $B$7Car Loans Amount Invested $ - $B$7>=0Binding $ - $B$8Personal Loans Amount Invested $ 162,500.00 $B$8>=0Not Binding $162,500.00 $B$8Personal Loans Amount Invested $ 162,500.00 $B$8 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: X 1 >0 X 2 >5and< 15 X 3 >8 and < 22 X 4 < 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 X 1 +700 X 2 +800 X 3 +1,000 X 4 < 40,000 Zoning restrictions only allow 40 or less units per location X 1 +5X 2 + 8X 3 + X 4 LP Model MAX:350 X 1 +450 X 2 +550 X 3 +750 X 4 Subject to:X 1 >0 X 2 >5 and < 15 X 3 >8 and < 22 X 4 < 10 500 X 1 +700 X 2 +800 X 3 +1,000 X 4 < 40,000 X 1 +5X 2 + 8X 3 + X 4 Decision Variables: X 11 : Newspaper to be used for Newsprint, X 12 : Newspaper to be used for Packaging. X 21 : Mixed Paper to be used for Newsprint, X 22 : Mixed Paper to be used for Packaging, X 23 : Mixed Paper to be used for Print Stock. X 31 : White Office Paper to be used for Newsprint, X 32 : White Office Paper to be used for Packaging, X 33 : White Office Paper to be used for Print Stock. X 41 : Cardboard to be used for Newsprint, X 42 : Cardboard to be used for Packaging. Objective functions: MIN (6.5+15)/.85 X 11 + (11+15)/.80 X 12 + (9.75+16)/.90 X 21 + (12.25+16)/.90 X 22 + (9.5+16)/.70 X 23 + (4.75+19)/.90 X 31 + (7.75+19)/.85 X 32 + (8.5+19)/.80 X 33 + (7.5+17)/.80 X 41 + (8.5+17)/.70 X 42 Simplifying: 25.29 X 11 + 32.5 X 12 + 28.61 X 21 + 31.39 X 22 + 36.43 X 23 + 26.39 X 31 + 31.47 X 32 + 34.38 X 33 + 30.63 X 41 + 36.43 X 42 Constrains: X 11 + X 21 + X 31 = 500, Newsprint that the company needs to produce. X 12 + X 22 + X 32 + X 42 = 600, Packaging that the company needs to produce. X 13 + X 23 + X 33 = 300, Print Stock that the company needs to produce. X 11 /.85 + X 12 /.80