SOLVE
abbey621
solver.xlsxLP_max
| Linear, Integer and Mixed Integer Programming | |||||||||||||
| Signs | |||||||||||||
| < | less than or equal to | ||||||||||||
| = | equals (You need to enter an apostrophe first.) | ||||||||||||
| > | greater than or equal to | ||||||||||||
| Data | Results | Problem setup area | |||||||||||
| S | M | L | LHS | Slack/Surplus | |||||||||
| Objective | $ 20.50 | $ 34.00 | $ 42.00 | sign | RHS | 651221.428571429 | < constraints | > constraints | |||||
| Min Demand for Small | 1 | > | 14000 | 16157.1428571429 | -2157.1428571429 | 0 | 0 | 16157.1428571429 | 14000 | ||||
| Max Demand for Small | 1 | < | 21000 | 16157.1428571429 | 4842.8571428571 | 16157.1428571429 | 21000 | 0 | 0 | ||||
| Min Demand for Medium | 1 | > | 6200 | 6200 | 0 | 0 | 0 | 6200 | 6200 | ||||
| Max Demand for Medium | 1 | < | 12500 | 6200 | 6300 | 6200 | 12500 | 0 | 0 | ||||
| Min Demand for Large | 1 | > | 2600 | 2600 | 0 | 0 | 0 | 2600 | 2600 | ||||
| Max Demand for Large | 1 | < | 4200 | 2600 | 1600 | 2600 | 4200 | 0 | 0 | ||||
| Bending/Forming Constraint | 0.4 | 0.7 | 0.8 | < | 23400 | 12882.8571428571 | 10517.1428571429 | 12882.8571428571 | 23400 | 0 | 0 | ||
| Welding Constraint | 0.6 | 1 | 1.2 | < | 23400 | 19014.2857142857 | 4385.7142857143 | 19014.2857142857 | 23400 | 0 | 0 | ||
| Painting Constraint | 1.4 | 2.6 | 3.1 | < | 46800 | 46800 | 0 | 46800 | 46800 | 0 | 0 | ||
| Results | |||||||||||||
| Variables | 16157.1428571429 | 6200 | 2600 | ||||||||||
| Objective | $ 651,221.43 | ||||||||||||
Answer Report 1
| Microsoft Excel 14.0 Answer Report | ||||||
| Worksheet: [Solver.xlsx]LP_max | ||||||
| Report Created: 4/17/2015 7:35:26 PM | ||||||
| Result: Solver found a solution. All Constraints and optimality conditions are satisfied. | ||||||
| Solver Engine | ||||||
| Engine: Simplex LP | ||||||
| Solution Time: 0.046 Seconds. | ||||||
| Iterations: 5 Subproblems: 0 | ||||||
| Solver Options | ||||||
| Max Time 100 sec, Iterations 100, Precision 0.000001 | ||||||
| Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 5%, Solve Without Integer Constraints, Assume NonNegative | ||||||
| Objective Cell (Max) | ||||||
| Cell | Name | Original Value | Final Value | |||
| $H$10 | RHS LHS | 0 | 651221.428571429 | |||
| Variable Cells | ||||||
| Cell | Name | Original Value | Final Value | Integer | ||
| $B$22 | Variables S | 0 | 16157.1428571429 | Contin | ||
| $C$22 | Variables M | 0 | 6200 | Contin | ||
| $D$22 | Variables L | 0 | 2600 | Contin | ||
| Constraints | ||||||
| Cell | Name | Cell Value | Formula | Status | Slack | |
| $K$11 | > < constraints | 0 | $K$11<=$L$11 | Binding | 0 | |
| $K$12 | < < constraints | 16157.1428571429 | $K$12<=$L$12 | Not Binding | 4842.8571428571 | |
| $K$13 | > < constraints | 0 | $K$13<=$L$13 | Binding | 0 | |
| $K$14 | < < constraints | 6200 | $K$14<=$L$14 | Not Binding | 6300 | |
| $K$15 | > < constraints | 0 | $K$15<=$L$15 | Binding | 0 | |
| $K$16 | < < constraints | 2600 | $K$16<=$L$16 | Not Binding | 1600 | |
| $K$17 | < < constraints | 12882.8571428571 | $K$17<=$L$17 | Not Binding | 10517.1428571429 | |
| $K$18 | < < constraints | 19014.2857142857 | $K$18<=$L$18 | Not Binding | 4385.7142857143 | |
| $K$19 | < < constraints | 46800 | $K$19<=$L$19 | Binding | 0 | |
| $M$11 | > > constraints | 16157.1428571429 | $M$11>=$N$11 | Not Binding | 2157.1428571429 | |
| $M$12 | < > constraints | 0 | $M$12>=$N$12 | Binding | 0 | |
| $M$13 | > > constraints | 6200 | $M$13>=$N$13 | Binding | 0 | |
| $M$14 | < > constraints | 0 | $M$14>=$N$14 | Binding | 0 | |
| $M$15 | > > constraints | 2600 | $M$15>=$N$15 | Binding | 0 | |
| $M$16 | < > constraints | 0 | $M$16>=$N$16 | Binding | 0 | |
| $M$17 | < > constraints | 0 | $M$17>=$N$17 | Binding | 0 | |
| $M$18 | < > constraints | 0 | $M$18>=$N$18 | Binding | 0 | |
| $M$19 | < > constraints | 0 | $M$19>=$N$19 | Binding | 0 |
Sensitivity Report 1
| Microsoft Excel 14.0 Sensitivity Report | |||||||
| Worksheet: [Solver.xlsx]LP_max | |||||||
| Report Created: 4/18/2015 7:35:27 PM | |||||||
| Variable Cells | |||||||
| Final | Reduced | Objective | Allowable | Allowable | |||
| Cell | Name | Value | Cost | Coefficient | Increase | Decrease | |
| $B$22 | Variables S | 16157.1428571429 | 0 | 20.5 | 1E+30 | 1.5322580645 | |
| $C$22 | Variables M | 6200 | 0 | 34 | 4.0714285714 | 1E+30 | |
| $D$22 | Variables L | 2600 | 0 | 42 | 3.3928571429 | 1E+30 | |
| Constraints | |||||||
| Final | Shadow | Constraint | Allowable | Allowable | |||
| Cell | Name | Value | Price | R.H. Side | Increase | Decrease | |
| $K$11 | > < constraints | 0 | 0 | 0 | 1E+30 | 0 | |
| $K$12 | < < constraints | 16157.1428571429 | 0 | 21000 | 1E+30 | 4842.8571428571 | |
| $K$13 | > < constraints | 0 | 0 | 0 | 1E+30 | 0 | |
| $K$14 | < < constraints | 6200 | 0 | 12500 | 1E+30 | 6300 | |
| $K$15 | > < constraints | 0 | 0 | 0 | 1E+30 | 0 | |
| $K$16 | < < constraints | 2600 | 0 | 4200 | 1E+30 | 1600 | |
| $K$17 | < < constraints | 12882.8571428571 | 0 | 23400 | 1E+30 | 10517.1428571429 | |
| $K$18 | < < constraints | 19014.2857142857 | 0 | 23400 | 1E+30 | 4385.7142857143 | |
| $K$19 | < < constraints | 46800 | 14.6429 | 46800 | 6780 | 3020 | |
| $M$11 | > > constraints | 16157.1428571429 | 0 | 14000 | 2157.1428571429 | 1E+30 | |
| $M$12 | < > constraints | 0 | 0 | 0 | 0 | 1E+30 | |
| $M$13 | > > constraints | 6200 | -4.0714 | 6200 | 1161.54 | 2607.69 | |
| $M$14 | < > constraints | 0 | 0 | 0 | 0 | 1E+30 | |
| $M$15 | > > constraints | 2600 | -3.3929 | 2600 | 974.1935483871 | 2187.10 | |
| $M$16 | < > constraints | 0 | 0 | 0 | 0 | 1E+30 | |
| $M$17 | < > constraints | 0 | 0 | 0 | 0 | 1E+30 | |
| $M$18 | < > constraints | 0 | 0 | 0 | 0 | 1E+30 | |
| $M$19 | < > constraints | 0 | 0 | 0 | 0 | 1E+30 |
Limits Report 1
| Microsoft Excel 14.0 Limits Report | |||||||||
| Worksheet: [Solver.xlsx]LP_max | |||||||||
| Report Created: 4/18/2015 7:35:27 PM | |||||||||
| Objective | |||||||||
| Cell | Name | Value | |||||||
| $H$10 | RHS LHS | 651221.428571429 | |||||||
| Variable | Lower | Objective | Upper | Objective | |||||
| Cell | Name | Value | Limit | Result | Limit | Result | |||
| $B$22 | Variables S | 16157.1428571429 | 14000 | 607000 | 16157.1428571261 | 651221.428571084 | |||
| $C$22 | Variables M | 6200 | 6200 | 651221.428571429 | 6200.0000000035 | 651221.428571547 | |||
| $D$22 | Variables L | 2600 | 2600 | 651221.428571429 | 2600.0000000012 | 651221.42857148 |
Question 2
| Maximize | Z = | 651221.428571429 | ||
| By Changing, | S = | 16157.1428571429 | ||
| M = | 6200 | |||
| L = | 2600 | |||
| Subject to, | ||||
| Min Demand for Small | 16157.1428571429 | >= | 14,000.00 | |
| Max Demand for Small | 16157.1428571429 | <= | 21,000.00 | |
| Min Demand for Medium | 6200 | >= | 6,200.00 | |
| Max Demand for Medium | 6200 | <= | 12,500.00 | |
| Min Demand for Large | 2600 | >= | 2,600.00 | |
| Max Demand for Large | 2600 | <= | 4,200.00 | |
| Bending/Forming Constraint | 12882.8571428571 | <= | 23,400.00 | |
| Welding Constraint | 19014.2857142857 | <= | 23,400.00 | |
| Painting Constraint | 46800 | <= | 46,800.00 |
Answer Report 2
| Microsoft Excel 14.0 Answer Report | ||||||
| Worksheet: [Solver.xlsx]Question 2 | ||||||
| Report Created: 4/19/2015 1:35:49 AM | ||||||
| Result: Solver found a solution. All Constraints and optimality conditions are satisfied. | ||||||
| Solver Engine | ||||||
| Engine: Simplex LP | ||||||
| Solution Time: 0.031 Seconds. | ||||||
| Iterations: 5 Subproblems: 0 | ||||||
| Solver Options | ||||||
| Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling | ||||||
| Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative | ||||||
| Objective Cell (Max) | ||||||
| Cell | Name | Original Value | Final Value | |||
| $D$3 | Z = | 0 | 651221.428571429 | |||
| Variable Cells | ||||||
| Cell | Name | Original Value | Final Value | Integer | ||
| $D$5 | S = | 0 | 16157.1428571429 | Contin | ||
| $D$6 | M = | 0 | 6200 | Contin | ||
| $D$7 | L = | 0 | 2600 | Contin | ||
| Constraints | ||||||
| Cell | Name | Cell Value | Formula | Status | Slack | |
| $C$10 | Min Demand for Small L = | 16157.1428571429 | $C$10>=$E$10 | Not Binding | 2157.1428571429 | |
| $C$11 | Max Demand for Small L = | 16157.1428571429 | $C$11<=$E$11 | Not Binding | 4842.8571428571 | |
| $C$12 | Min Demand for Medium L = | 6200 | $C$12>=$E$12 | Binding | 0 | |
| $C$13 | Max Demand for Medium L = | 6200 | $C$13<=$E$13 | Not Binding | 6300 | |
| $C$14 | Min Demand for Large L = | 2600 | $C$14>=$E$14 | Binding | 0 | |
| $C$15 | Max Demand for Large L = | 2600 | $C$15<=$E$15 | Not Binding | 1600 | |
| $C$16 | Bending/Forming Constraint L = | 12882.8571428571 | $C$16<=$E$16 | Not Binding | 10517.1428571429 | |
| $C$17 | Welding Constraint L = | 19014.2857142857 | $C$17<=$E$17 | Not Binding | 4385.7142857143 | |
| $C$18 | Painting Constraint L = | 46800 | $C$18<=$E$18 | Binding | 0 |
Sensitivity Report 2
| Microsoft Excel 14.0 Sensitivity Report | |||||||
| Worksheet: [Solver.xlsx]Question 2 | |||||||
| Report Created: 4/19/2015 1:35:49 AM | |||||||
| Variable Cells | |||||||
| Final | Reduced | Objective | Allowable | Allowable | |||
| Cell | Name | Value | Cost | Coefficient | Increase | Decrease | |
| $D$5 | S = | 16157.1428571429 | 0 | 20.5 | 1E+30 | 1.5322580645 | |
| $D$6 | M = | 6200 | 0 | 34 | 4.0714285714 | 1E+30 | |
| $D$7 | L = | 2600 | 0 | 42 | 3.3928571429 | 1E+30 | |
| Constraints | |||||||
| Final | Shadow | Constraint | Allowable | Allowable | |||
| Cell | Name | Value | Price | R.H. Side | Increase | Decrease | |
| $C$10 | Min Demand for Small L = | 16157.1428571429 | 0 | 14000 | 2157.1428571429 | 1E+30 | |
| $C$11 | Max Demand for Small L = | 16157.1428571429 | 0 | 21000 | 1E+30 | 4842.8571428571 | |
| $C$12 | Min Demand for Medium L = | 6200 | -4.0714285714 | 6200 | 1161.5384615385 | 2607.6923076923 | |
| $C$13 | Max Demand for Medium L = | 6200 | 0 | 12500 | 1E+30 | 6300 | |
| $C$14 | Min Demand for Large L = | 2600 | -3.3928571429 | 2600 | 974.1935483871 | 2187.0967741936 | |
| $C$15 | Max Demand for Large L = | 2600 | 0 | 4200 | 1E+30 | 1600 | |
| $C$16 | Bending/Forming Constraint L = | 12882.8571428571 | 0 | 23400 | 1E+30 | 10517.1428571429 | |
| $C$17 | Welding Constraint L = | 19014.2857142857 | 0 | 23400 | 1E+30 | 4385.7142857143 | |
| $C$18 | Painting Constraint L = | 46800 | 14.6428571429 | 46800 | 6780 | 3020 |
Limits Report 2
| Microsoft Excel 14.0 Limits Report | |||||||||
| Worksheet: [Solver.xlsx]Question 2 | |||||||||
| Report Created: 4/19/2015 1:35:49 AM | |||||||||
| Objective | |||||||||
| Cell | Name | Value | |||||||
| $D$3 | Z = | 651221.428571429 | |||||||
| Variable | Lower | Objective | Upper | Objective | |||||
| Cell | Name | Value | Limit | Result | Limit | Result | |||
| $D$5 | S = | 16157.1428571429 | 14000 | 607000 | 16157.1428571261 | 651221.428571084 | |||
| $D$6 | M = | 6200 | 6200 | 651221.428571429 | 6200.0000000035 | 651221.428571547 | |||
| $D$7 | L = | 2600 | 2600 | 651221.428571429 | 2600.0000000012 | 651221.42857148 |
