LP formulation for Pottery Problem
Resource Requirements
Labor Clay Revenue
Product (hr/unit) (lb/unit) ($/unit)
Bowl 1 4 40
Mug 2 3 50
There are 40 hours of labor available per day
There are 120 pounds of clay available per day
How many bowls and how many mugs to make daily to maximize revenue?
The optimization model:
B M
Units made: 24 8
MAX 40 50 1360 Total Revenue
Total
subject to Usage Available
1 2 40 40 labor
4 3 120 120 clay
Microsoft Excel 10.0 Answer Report
Worksheet: [In-Class LP Examples.xls]Pottery Problem
Report Created: 10/30/2002 10:01:46 AM
Target Cell (Max)
Cell Name Original Value Final Value
$F$17 MAX 1360 1360
Adjustable Cells
Cell Name Original Value Final Value
$D$16 Units made: B 24 24
$E$16 Units made: M 8 8
Constraints
Cell Name Cell Value Formula Status Slack
$F$19 Total Usage 40 $F$19<=$G$19 Binding 0
$F$20 Total Usage 120 $F$20<=$G$20 Binding 0
Microsoft Excel 10.0 Sensitivity Report
Worksheet: [In-Class LP Examples.xls]Pottery Problem
Report Created: 10/30/2002 10:01:47 AM
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$D$16 Units made: B 24 0 40 26.66666667 15
$E$16 Units made: M 8 0 50 30 20
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$F$19 Total Usage 40 16 40 40 10
$F$20 Total Usage 120 6 120 40 60
LP Lego Problem Formulation
Resource Requirements
Large Small Revenue
Product Legos Legos ($/unit)
Table 2 2 16
Chair 1 2 10
There are 6 large legos available
There are 8 small legos available
How many tables and how many chairs to make daily to maximize revenue?
The optimization model:
T C
Units made: 3 0
MAX 10 10 30 Total Revenue
Total
subject to Usage Available
2 1 6 6 Large Legos
2 2 6 8 Small Legos
Microsoft Excel 10.0 Answer Report
Worksheet: [In-Class LP Examples.xls]Lego Problem
Report Created: 10/30/2002 10:02:38 AM
Target Cell (Max)
Cell Name Original Value Final Value
$F$17 MAX 52 52
Adjustable Cells
Cell Name Original Value Final Value
$D$16 Units made: T 2 2
$E$16 Units made: C 2 2
Constraints
Cell Name Cell Value Formula Status Slack
$F$19 Total Usage 6 $F$19<=$G$19 Binding 0
$F$20 Total Usage 8 $F$20<=$G$20 Binding 0
Microsoft Excel 10.0 Sensitivity Report
Worksheet: [In-Class LP Examples.xls]Lego Problem
Report Created: 10/30/2002 10:02:38 AM
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$D$16 Units made: T 2 0 16 4 6
$E$16 Units made: C 2 0 10 6 2
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$F$19 Total Usage 6 6 6 2 2
$F$20 Total Usage 8 2 8 4 2