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Question 2 - Solution

The Excel solver found an optimal solution for a linear programming problem that maximized profit with variables of units produced of products x1, x2, and x3, subject to 4 constraints on resource usage. The optimal solution was to produce 32 units of x1 and 34 units of x3, with an objective value (maximum profit) of 660. The solver took 3 iterations and 0.016 seconds to find this optimal solution satisfying all constraints.

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38 views5 pages

Question 2 - Solution

The Excel solver found an optimal solution for a linear programming problem that maximized profit with variables of units produced of products x1, x2, and x3, subject to 4 constraints on resource usage. The optimal solution was to produce 32 units of x1 and 34 units of x3, with an objective value (maximum profit) of 660. The solver took 3 iterations and 0.016 seconds to find this optimal solution satisfying all constraints.

Uploaded by

seemabzafar33
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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Microsoft Excel 16.

0 Answer Report
Worksheet: [Book5]Sheet1
Report Created: 23/02/2024 00:06:38
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 3 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$15 Max Profit x1 0 660

Variable Cells
Cell Name Original Value Final Value Integer
$B$13 Units produced x1 0 32 Contin
$C$13 Units produced x2 0 0 Contin
$D$13 Units produced x3 0 34 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$18 #1 Amount used 134 $B$18<=300 Not Binding 166
$B$19 #2 Amount used 200 $B$19<=$D$19 Binding 0
$B$20 #3 Amount used 160 $B$20<=$D$20 Binding 0
$B$21 #4 Amount used 34 $B$21>=10 Not Binding 24
NonNegative
Microsoft Excel 16.0 Sensitivity Report
Worksheet: [Book5]Sheet1
Report Created: 23/02/2024 00:06:38

Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$13 Units produced x1 32 0 10 1E+030 4.21875
$C$13 Units produced x2 0 -6.75 10 6.75 1E+030
$D$13 Units produced x3 34 0 10 10 10

Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$B$18 #1 Amount used 134 0 300 1E+030 166
$B$19 #2 Amount used 200 2.5 200 221.33333333 96
$B$20 #3 Amount used 160 1 160 240 160
$B$21 #4 Amount used 34 0 10 24 1E+030
Microsoft Excel 16.0 Limits Report
Worksheet: [Book5]Sheet1
Report Created: 23/02/2024 00:06:38

Objective
Cell Name Value
$B$15 Max Profit x1 660

Variable Lower Objective Upper Objective


Cell Name Value Limit Result Limit Result
$B$13 Units produced x1 32 0 340 32 660
$C$13 Units produced x2 0 0 660 0 660
$D$13 Units produced x3 34 10 420 34 660
Question 2
LHS Coefficients RHS
x1 x2 x3 Values
#1 1 5 3 <= 300
#2 2 3.5 4 <= 200
#3 5 8 0 <= 160
#4 0 0 1 >= 10

Objective function 10 10 10

Decision Variables
x1 x2 x3
Units produced 32 0 34

Max Profit 660

Constraints Amount used RHS


#1 134 <= 300
#2 200 <= 200
#3 160 <= 160
#4 34 >= 10

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