Merton Truck CompanyTABLE AMachine-hours: Requirements and availability

Machine-hoursRequired per Truck Total machine-hours

Department Model 101 Model 102 Available per Month

Engine assembly 1.0 2.0 4,000Metal stamping 2.0 2.0 6,000Model 101 assembly 2.0 - 5,000Model 102 assembly - 3.0 4,500

TABLE BStandard Product Costs

Model 101 Model 102Direct materials $24,000 $20,000Direct Labour

Engine assembly $1,200 $2,400Metal stamping $800 $600Final assembly $2,000 $1,500

$4,000 $4,500Overhead

Engine assembly $2,525 $4,850Metal stamping $3,480 $3,080Final assembly $6,200 $3,500

$12,205 $11,430Total $40,205 $35,930

Microsoft Excel 9.0 Answer ReportWorksheet: [Merton Truck Company.xls]Q1Report Created: 9/4/2007 12:23:23 AM

Target Cell (Max)Cell Name Original Value Final Value

$G$3 Obj Function Profit 0 11000000

Adjustable CellsCell Name Original Value Final Value

$E$4 Decsion Variables M101 0 2000$F$4 Decsion Variables M102 0 1000

ConstraintsCell Name Cell Value Formula Status Slack

$G$6 Engine Assembly Hrs used 4000 $G$6<=$I$6 Binding 0$G$7 Metal Stamping Hrs used 6000 $G$7<=$I$7 Binding 0$G$19 Engine Assembly Utilised 4,001 $G$19<=$I$19 Not Binding 1000$G$9 Model 102 Assembly Hrs used 3000 $G$9<=$I$9 Not Binding 1500

Microsoft Excel 9.0 Sensitivity ReportWorksheet: [Merton Truck Company.xls]Q1Report Created: 9/4/2007 12:23:23 AM

Adjustable CellsFinal Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease$E$4 Decsion Variables M101 2000 0 3000 2000 500$F$4 Decsion Variables M102 1000 0 5000 1000 2000

ConstraintsFinal Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease$G$6 Engine Assembly Hrs used 4000 2000 4000 500 500$G$7 Metal Stamping Hrs used 6000 0 6000 500 1000$G$19 Engine Assembly Utilised 4,001 0 5000 1E+030 1000$G$9 Model 102 Assembly Hrs used 3000 1 4500 1E+030 1500

Microsoft Excel 9.0 Limits ReportWorksheet: [Merton Truck Company.xls]Q1Report Created: 9/4/2007 12:23:23 AM

TargetCell Name Value

$G$3 Obj Function Profit 11000000

Adjustable Lower Target Upper TargetCell Name Value Limit Result Limit Result

$E$4 Decsion Variables M101 2000 0 5000000 2000.000005 11000000.02$F$4 Decsion Variables M102 1000 0 6000000 1000.000003 11000000.01

Q 1(a) M101 M102 ProfitObj Function 3000 5000 11000000Decsion Variables 2000 1000

Constraints Hrs req/Unit Hrs used Relation Hr Avl Unused (hrs)Engine Assembly 1 2 4000 <= 4000 0Metal Stamping 2 2 6000 <= 6000 0Model 101 Assembly 2 0 4000 <= 5000 1000Model 102 Assembly 0 3 3000 <= 4500 1500

>=0 >=0

Q 1(b)>=0 >=0

Model 101 Model 102 ProfitObjective function 3,000 5,000 11,002,000

Decision Variables 1,999 1,001Machine-hours

Constraints Required/unit Utilised Relation Maximum available UnutilisedEngine Assembly 1 2 4,001 <= 4,001 0Metal Stamping 2 2 6,000 <= 6,000 0Model 101 assembly 2 0 3,998 <= 5,000 1,002Model 102 assembly 0 3 3,003 <= 4,500 1,497Worth of extra unit of capacity 2,000

Q 1(c)>=0 >=0

Model 101 Model 102 ProfitObjective function 3,000 5,000 11,200,000

Decision Variables 1,900 1,100Machine-hours

Constraints Required/unit Utilised Relation Maximum available UnutilisedEngine Assembly 1 2 4,100 <= 4,100 0Metal Stamping 2 2 6,000 <= 6,000 0Model 101 assembly 2 0 3,800 <= 5,000 1,200Model 102 assembly 0 3 3,300 <= 4,500 1,200

Value of 1 additional unit 2,000Value of 100 additional unit 200000

Q 1(d)>=0 >=0

Model 101 Model 102 ProfitObjective function 3,000 5,000 12,000,000

Decision Variables 1,500 1,500Machine-hours

Constraints Required/unit Utilised Relation Maximum available UnutilisedEngine Assembly 1 2 4,500 <= 4,501 1Metal Stamping 2 2 6,000 <= 6,000 0Model 101 assembly 2 0 3,000 <= 5,000 2,000Model 102 assembly 0 3 4,500 <= 4,500 0

Q 2>=0 >=0

Model 101 Model 102 ProfitObjective function 3,000 5,000 12,000,000

Decision Variables 1,500 1,500Machine-hours

Constraints Required/unit Utilised Relation Maximum available UnutilisedEngine Assembly 1 2 4,500Metal Stamping 2 2 6,000 <= 6,000 0Model 101 assembly 2 0 3,000 <= 5,000 2,000Model 102 assembly 0 3 4,500 <= 4,500 0

Maximum Machine hours rented 500

Q 3(a)>=0 >=0 >=0

Model 101 Model 102 Model 103 ProfitObjective function 3,000 5,000 2,000 11,000,000

Decision Variables 2,000 1,000 0Machine-hours

Constraints Required/unit Utilised Relation Maximum available UnutilisedEngine Assembly 1 2 0.8 4,000 <= 4,000 0Metal Stamping 2 2 1.5 6,000 <= 6,000 0Model 101 assembly 2 0 1 4,000 <= 5,000 1,000Model 102 assembly 0 3 0 3,000 <= 4,500 1,500

No they should not produce Model 103

Q 3(b)

The contribution of each Model 103 truck has to be increased by $350(See worksheet 3b) before it becomes worthwhile to produce any unit

Microsoft Excel 9.0 Answer ReportWorksheet: [Merton Truck Company.xls]Q3Report Created: 9/3/2007 11:33:51 PM

Target Cell (Max)Cell Name Original Value Final Value

$H$4 Objective function Profit 11,000,000 11,000,000

Adjustable CellsCell Name Original Value Final Value

$E$5 Decision Variables Model 101 2,000 2,000$F$5 Decision Variables Model 102 1,000 1,000$G$5 Decision Variables Model 103 0 0

ConstraintsCell Name Cell Value Formula Status Slack

$H$8 Engine assembly constraint Utilised 4,000 $H$8<=$J$8 Binding 0$H$9 Metal stamping constraint Utilised 6,000 $H$9<=$J$9 Binding 0$H$10 Model 101 assembly constraint Utilised 4,000 $H$10<=$J$10 Not Binding 1000$H$11 Model 102 assembly constraint Utilised 3,000 $H$11<=$J$11 Not Binding 1500$E$5 Decision Variables Model 101 2,000 $E$5>=0 Not Binding 2,000$F$5 Decision Variables Model 102 1,000 $F$5>=0 Not Binding 1,000$G$5 Decision Variables Model 103 0 $G$5>=0 Binding 0

Microsoft Excel 9.0 Sensitivity ReportWorksheet: [Merton Truck Company.xls]Q3Report Created: 9/3/2007 11:33:51 PM

Adjustable CellsFinal Reduced Objective Allowable

Cell Name Value Cost Coefficient Increase$E$5 Decision Variables Model 101 2,000 0 3000 2000$F$5 Decision Variables Model 102 1,000 0 5000 1000$G$5 Decision Variables Model 103 0 -350 2000 350

ConstraintsFinal Shadow Constraint Allowable

Cell Name Value Price R.H. Side Increase$H$8 Engine assembly constraint Utilised 4,000 2,000 4000 500$H$9 Metal stamping constraint Utilised 6,000 500 6000 500$H$10 Model 101 assembly constraint Utilised 4,000 0 5000 1E+030$H$11 Model 102 assembly constraint Utilised 3,000 0 4500 1E+030

AllowableDecrease

499.99999992000

1E+030

AllowableDecrease

500100010001500

Microsoft Excel 9.0 Limits ReportWorksheet: [Merton Truck Company.xls]Q3Report Created: 9/3/2007 11:33:51 PM

TargetCell Name Value

$H$4 Objective function Profit 11,000,000

Adjustable Lower Target Upper TargetCell Name Value Limit Result Limit Result

$E$5 Decision Variables Model 101 2,000 0 5,000,000 2,000 11,000,000$F$5 Decision Variables Model 102 1,000 0 6,000,000 1,000 11,000,000$G$5 Decision Variables Model 103 0 0 11,000,000 0 11,000,000

Q 4>=0 >=0

Model 101 Model 102 Profit Net ProfitObjective function 3,000 5,000 12000000 1,750,000

Decision Variables 1,500 1,500Machine-hours

Constraints Required/unit Utilised Relation Maximum available UnutilisedEngine Assembly 1 2 4,500 <= 6,000 1,500Metal Stamping 2 2 6,000 <= 6,000 0Model 101 assembly 2 0 3,000 <= 5,000 2,000Model 102 assembly 0 3 4,500 <= 4,500 0

Overtime is not advisable Since operating overtime reduces the profits(earlier net profit was 2,400,000 now it has reduced to 1,750,000)

Microsoft Excel 9.0 Answer ReportWorksheet: [Merton Truck Company.xls]Q4Report Created: 9/3/2007 11:39:56 PM

Target Cell (Max)Cell Name Original Value Final Value

$I$4 Objective function Net Profit -2,150,000 1,750,000

Adjustable CellsCell Name Original Value Final Value

$E$5 Decision Variables Model 101 0 1,500$F$5 Decision Variables Model 102 0 1,500

ConstraintsCell Name Cell Value Formula Status Slack

$G$8 Engine assembly constraint Utilised 4,500 $G$8<=$I$8 Not Binding 1500$G$9 Metal stamping constraint Utilised 6,000 $G$9<=$I$9 Binding 0$G$10 Model 101 assembly constraint Utilised 3,000 $G$10<=$I$10 Not Binding 2000$G$11 Model 102 assembly constraint Utilised 4,500 $G$11<=$I$11 Binding 0$E$5 Decision Variables Model 101 1,500 $E$5>=0 Not Binding 1,500$F$5 Decision Variables Model 102 1,500 $F$5>=0 Not Binding 1,500

Microsoft Excel 9.0 Sensitivity ReportWorksheet: [Merton Truck Company.xls]Q4Report Created: 9/3/2007 11:39:56 PM

Adjustable CellsFinal Reduced

Cell Name Value Gradient$E$5 Decision Variables Model 101 1,500 0$F$5 Decision Variables Model 102 1,500 0

ConstraintsFinal Lagrange

Cell Name Value Multiplier$G$8 Engine assembly constraint Utilised 4,500 0$G$9 Metal stamping constraint Utilised 6,000 600$G$10 Model 101 assembly constraint Utilised 3,000 0$G$11 Model 102 assembly constraint Utilised 4,500 67

Microsoft Excel 9.0 Limits ReportWorksheet: [Merton Truck Company.xls]Q4Report Created: 9/3/2007 11:39:56 PM

TargetCell Name Value

$I$4 Objective function Net Profit 1,750,000

Adjustable Lower Target Upper TargetCell Name Value Limit Result Limit Result

$E$5 Decision Variables Model 101 1,500 0 -50,000 1,500 1,750,000$F$5 Decision Variables Model 102 1,500 0 -350,000 1,500 1,750,000

Microsoft Excel 9.0 Answer ReportWorksheet: [Merton Truck Company.xls]Q5Report Created: 9/4/2007 12:40:16 AM

Target Cell (Max)Cell Name Original Value Final Value

$G$4 Objective function Profit 11,000,000 10,500,000

Adjustable CellsCell Name Original Value Final Value

$E$5 Decision variables Model 101 2,000 2,250$F$5 Decision variables Model 102 1,000 750

ConstraintsCell Name Cell Value Formula Status Slack

$G$8 Engine Assembly Utilised 3,750 $G$8<=$I$8 Not Binding 250$G$9 Metal Stamping Utilised 6,000 $G$9<=$I$9 Binding 0$G$10 Model 101 assembly Utilised 4,500 $G$10<=$I$10 Not Binding 500$G$11 Model 102 assembly Utilised 2,250 $G$11<=$I$11 Not Binding 2250$G$12 Additional constraint Utilised 0 $G$12>=$I$12 Binding 0$E$5 Decision variables Model 101 2,250 $E$5>=0 Not Binding 2,250$F$5 Decision variables Model 102 750 $F$5>=0 Not Binding 750

Microsoft Excel 9.0 Sensitivity ReportWorksheet: [Merton Truck Company.xls]Q5Report Created: 9/4/2007 12:40:16 AM

Adjustable CellsFinal Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease$E$5 Decision variables Model 101 2,250 0 3000 2000 4666.666667$F$5 Decision variables Model 102 750 0 5000 1E+030 2000

ConstraintsFinal Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease$G$8 Engine Assembly Utilised 3,750 0 4000 1E+030 250$G$9 Metal Stamping Utilised 6,000 1,750 6000 400 6000$G$10 Model 101 assembly Utilised 4,500 0 5000 1E+030 500$G$11 Model 102 assembly Utilised 2,250 0 4500 1E+030 2250$G$12 Additional constraint Utilised 0 -500 0 1000 1000

Microsoft Excel 9.0 Limits ReportWorksheet: [Merton Truck Company.xls]Q5Report Created: 9/4/2007 12:40:16 AM

TargetCell Name Value

$G$4 Objective function Profit 10,500,000

Adjustable Lower Target Upper TargetCell Name Value Limit Result Limit Result

$E$5 Decision variables Model 101 2,250 2,250 10,500,000 2,250 10,500,000$F$5 Decision variables Model 102 750 0 6,750,000 #N/A #N/A

Q 5>=0 >=0

Model 101 Model 102 ProfitObjective function 3,000 5,000 10,500,000

Decision variables 2,250 750Machine-hours

Constraints Required/unit Utilised Relation Maximum available UnutilisedEngine Assembly 1 2 3,750 <= 4,000 250Metal Stamping 2 2 6,000 <= 6,000 0Model 101 assembly 2 0 4,500 <= 5,000 500Model 102 assembly 0 3 2,250 <= 4,500 2,250Additional constraint 1 -3 0 >= 0 0