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Decision Variables X X Objective Value Value 250 0 5000 Coefficients 20 15

The document presents an optimization problem to maximize profit by allocating customers to three plants within supply and demand constraints. It shows the optimal solution allocating specific customer demand quantities across the plants while satisfying all constraints, with an objective value of 27190. The summary also includes constraints on plant supply and customer demand.

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42 views15 pages

Decision Variables X X Objective Value Value 250 0 5000 Coefficients 20 15

The document presents an optimization problem to maximize profit by allocating customers to three plants within supply and demand constraints. It shows the optimal solution allocating specific customer demand quantities across the plants while satisfying all constraints, with an objective value of 27190. The summary also includes constraints on plant supply and customer demand.

Uploaded by

gaoiranally
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
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Decision Variables x₁ x₂ OBJECTIVE VALUE

Value 250 0 5000


Coefficients 20 15

LHS RHS
CONSTRAINTS 1 200 150 50000 ≤ 50000

THE MAXIMUM VALUE OF PROFIT IS 5000 WITH X₁= 250 and X₂= 0
Maximize= P=20x+15y

Constraints
200x + 150y≤ 50000
x,y≥0
Decision Variables x₁ x₂
Value 0 2
Coefficients 5 7

CONSTRAINTS 1 2 3
CONSTRAINTS 2 3 -1
CONSTRAINTS 3 -1 1
CONSTRAINTS 4 2 5
OBJECTIVE VALUE Minimize z= 5x+7y
14 constraints
2x + 3y≥6
3x-y≤15
(-x)+y≤4
2x+5y≤ 27
x,y≥0

LHS RHS
6 ≥ 6
-2 ≤ 15
2 ≤ 4
10 ≤ 27
Microsoft Excel 15.0 Answer Report
Worksheet: [1&2 OR.xlsx]Sheet1
Report Created: 23/01/2024 10:02:15 am
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.031 Seconds.
Iterations: 9 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 (Min)


Cell Name Original Value Final Value
$B$18 OFV = 0 21990

Variable Cells
Cell Name Original Value Final Value Integer
$B$10 Plant 1 Customer 1 0 0 Contin
$C$10 Plant 1 Customer 2 0 0 Contin
$D$10 Plant 1 Customer 3 0 500 Contin
$E$10 Plant 1 Customer 4 0 100 Contin
$B$11 Plant 2 Customer 1 0 250 Contin
$C$11 Plant 2 Customer 2 0 330 Contin
$D$11 Plant 2 Customer 3 0 0 Contin
$E$11 Plant 2 Customer 4 0 0 Contin
$B$12 Plant 3 Customer 1 0 0 Contin
$C$12 Plant 3 Customer 2 0 50 Contin
$D$12 Plant 3 Customer 3 0 0 Contin
$E$12 Plant 3 Customer 4 0 450 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$13 Demand Customer 1 250 $B$13=$B$15 Binding 0
$C$13 Demand Customer 2 380 $C$13=$C$15 Binding 0
$D$13 Demand Customer 3 500 $D$13=$D$15 Binding 0
$E$13 Demand Customer 4 550 $E$13=$E$15 Binding 0
$F$10 Plant 1 Supply 600 $F$10<=$H$10 Binding 0
$F$11 Plant 2 Supply 580 $F$11<=$H$11 Not Binding 120
$F$12 Plant 3 Supply 500 $F$12<=$H$12 Binding 0
Microsoft Excel 15.0 Answer Report
Worksheet: [1&2 OR.xlsx]Sheet1 (2)
Report Created: 23/01/2024 10:28:18 am
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.031 Seconds.
Iterations: 14 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
$B$18 OFV = 0 27190

Variable Cells
Cell Name Original Value Final Value Integer
$B$10 Plant 1 Customer 1 0 220 Contin
$C$10 Plant 1 Customer 2 0 380 Contin
$D$10 Plant 1 Customer 3 0 0 Contin
$E$10 Plant 1 Customer 4 0 0 Contin
$B$11 Plant 2 Customer 1 0 0 Contin
$C$11 Plant 2 Customer 2 0 0 Contin
$D$11 Plant 2 Customer 3 0 500 Contin
$E$11 Plant 2 Customer 4 0 200 Contin
$B$12 Plant 3 Customer 1 0 30 Contin
$C$12 Plant 3 Customer 2 0 0 Contin
$D$12 Plant 3 Customer 3 0 0 Contin
$E$12 Plant 3 Customer 4 0 350 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$13 Demand Customer 1 250 $B$13=$B$15 Binding 0
$C$13 Demand Customer 2 380 $C$13=$C$15 Binding 0
$D$13 Demand Customer 3 500 $D$13=$D$15 Binding 0
$E$13 Demand Customer 4 550 $E$13=$E$15 Binding 0
$F$10 Plant 1 Supply 600 $F$10<=$H$10 Binding 0
$F$11 Plant 2 Supply 700 $F$11<=$H$11 Binding 0
$F$12 Plant 3 Supply 380 $F$12<=$H$12 Not Binding 120
Customer 1 Customer 2 Customer 3 Customer 4 Supply
Plant 1 18 16 10 14 600
Plant 2 14 13 15 18 700
Plant 3 15 12 12 16 500
Demand 250 380 500 550

Customer 1 Customer 2 Customer 3 Customer 4 Supply Sign Supply


Plant 1 220 380 0 0 600 ≤ 600
Plant 2 0 0 500 200 700 ≤ 700
Plant 3 30 0 0 350 380 ≤ 500
Demand 250 380 500 550 1800
Sign = = = =
Demand 250 380 500 550 1680 120

OFV 27190
Microsoft Excel 15.0 Answer Report
Worksheet: [1&2 OR.xlsx]Sheet3
Report Created: 23/01/2024 10:34:04 am
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.047 Seconds.
Iterations: 8 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 (Min)


Cell Name Original Value Final Value
$B$18 OFV = 0 17100

Variable Cells
Cell Name Original Value Final Value Integer
$B$10 Plant 1 Customer 1 0 0 Contin
$C$10 Plant 1 Customer 2 0 0 Contin
$D$10 Plant 1 Customer 3 0 500 Contin
$E$10 Plant 1 Customer 4 0 100 Contin
$B$11 Plant 2 Customer 1 0 250 Contin
$C$11 Plant 2 Customer 2 0 380 Contin
$D$11 Plant 2 Customer 3 0 0 Contin
$E$11 Plant 2 Customer 4 0 0 Contin
$B$12 Plant 3 Customer 1 0 0 Contin
$C$12 Plant 3 Customer 2 0 0 Contin
$D$12 Plant 3 Customer 3 0 0 Contin
$E$12 Plant 3 Customer 4 0 450 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$13 Demand Customer 1 250 $B$13=$B$15 Binding 0
$C$13 Demand Customer 2 380 $C$13=$C$15 Binding 0
$D$13 Demand Customer 3 500 $D$13=$D$15 Binding 0
$E$13 Demand Customer 4 550 $E$13=$E$15 Binding 0
$F$10 Plant 1 Supply 600 $F$10<=$H$10 Binding 0
$F$11 Plant 2 Supply 630 $F$11<=$H$11 Not Binding 70
$F$12 Plant 3 Supply 450 $F$12<=$H$12 Not Binding 50
Customer 1 Customer 2 Customer 3 Customer 4 Supply
Plant 1 18 16 10 14 600
Plant 2 14 0 15 18 700
Plant 3 15 12 12 16 500
Demand 250 380 500 550

Customer 1 Customer 2 Customer 3 Customer 4 Supply Sign Supply


Plant 1 0 0 500 100 600 ≤ 600
Plant 2 250 380 0 0 630 ≤ 700
Plant 3 0 0 0 450 450 ≤ 500
Demand 250 380 500 550 1800
Sign = = = =
Demand 250 380 500 550 1680 120

OFV 17100
Customer 1 Customer 2 Customer 3 Customer 4 Supply
Plant 1 18 16 10 14 600
Plant 2 14 13 15 18 700
Plant 3 15 12 12 16 500
Demand 250 380 500 550

Customer 1 Customer 2 Customer 3 Customer 4 Supply Sign Supply


Plant 1 0 0 500 100 600 ≤ 600
Plant 2 250 330 0 0 580 ≤ 700
Plant 3 0 50 0 450 500 ≤ 500
Demand 250 380 500 550 1800
Sign = = = =
Demand 250 380 500 550 1680 120

OFV 21990
Microsoft Excel 15.0 Answer Report
Worksheet: [1&2 OR.xlsx]Sheet4
Report Created: 29/01/2024 8:22:11 pm
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.031 Seconds.
Iterations: 8 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)


Cell Name Original Value Final Value
$B$18 OFV = 0 21990

Variable Cells
Cell Name Original Value Final Value Integer
$B$10 Plant 1 Customer 1 0 0 Contin
$C$10 Plant 1 Customer 2 0 0 Contin
$D$10 Plant 1 Customer 3 0 500 Contin
$E$10 Plant 1 Customer 4 0 100 Contin
$B$11 Plant 2 Customer 1 0 250 Contin
$C$11 Plant 2 Customer 2 0 330 Contin
$D$11 Plant 2 Customer 3 0 0 Contin
$E$11 Plant 2 Customer 4 0 0 Contin
$B$12 Plant 3 Customer 1 0 0 Contin
$C$12 Plant 3 Customer 2 0 50 Contin
$D$12 Plant 3 Customer 3 0 0 Contin
$E$12 Plant 3 Customer 4 0 450 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$13 Demand Customer 1 250 $B$13=$B$15 Binding 0
$C$13 Demand Customer 2 380 $C$13=$C$15 Binding 0
$D$13 Demand Customer 3 500 $D$13=$D$15 Binding 0
$E$13 Demand Customer 4 550 $E$13=$E$15 Binding 0
$F$10 Plant 1 Supply 600 $F$10<=$H$10 Binding 0
$F$11 Plant 2 Supply 580 $F$11<=$H$11 Not Binding 120
$F$12 Plant 3 Supply 500 $F$12<=$H$12 Binding 0
Customer 1 Customer 2 Customer 3 Customer 4 Supply
Plant 1 18 16 10 14 600
Plant 2 14 13 15 18 700
Plant 3 15 12 12 16 500
Demand 250 380 500 550

Customer 1 Customer 2 Customer 3 Customer 4 Supply Sign


Plant 1 0 0 500 100 600 ≤
Plant 2 250 330 0 0 580 ≤
Plant 3 0 50 0 450 500 ≤
Demand 250 380 500 550
Sign = = = =
Demand 250 380 500 550 1680

OFV 21990
Supply
600
700
500
1800

120
Customer 1 Customer 2 Customer 3 Customer 4 Supply
Plant 1 18 16 10 14 600
Plant 2 14 13 15 18 700
Plant 3 15 12 12 16 500
Demand 250 380 500 550

Customer 1 Customer 2 Customer 3 Customer 4 Supply


Plant 1 0 0 500 100 600
Plant 2 250 330 0 0 580
Plant 3 0 50 0 450 500
Demand 250 380 500 550
Sign = = = =
Demand 250 380 500 550 1680

OFV 21990
Sign Supply
≤ 600
≤ 700
≤ 500
1800

120

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