X1 X2 X3 X4 MAX VALUE
COEFF 20 15 18 10
VALUES 0 27 0 35.25 757.5
LHS SIGN RHS
CONST 1 4 -3 10 4 60 <= 60
CONST 2 1 1 1 0 27 = 27
CONST 3 0 -1 4 7 219.75 >= 35
2X1 + 4X2 >= -12 MULTIPLY BOTH SIDES WITH -1 -2X1 - 4X2 <= 12
X1 X2 X3 MIN VALUE
COEFF 2 -3 6
VALUE 6.2 11.6 0 -22.4
LHS SIGN RHS
CONST 1 3 -1 2 7 <= 7
CONST 2 -2 -4 0 -58.8 <= 12
CONST 3 -4 3 8 10 <= 10
Microsoft Excel 14.0 Answer Report
Worksheet: [LPP2.xlsx]QUES 3
Report Created: 10/16/2023 4:24:14 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 2 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$12 VALUE MAX VALUE 0 1500
Variable Cells
Cell Name Original Value Final Value Integer
$B$12 VALUE X 0 50 Contin
$C$12 VALUE Y 0 0 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$D$14 M1 CONST LHS 200 $D$14<=$F$14 Binding 0
$D$15 M2 CONST LHS 250 $D$15<=$F$15 Not Binding 150
Microsoft Excel 14.0 Sensitivity Report
Worksheet: [LPP2.xlsx]QUES 3
Report Created: 10/16/2023 4:24:14 PM
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$12 VALUE X 50 0 30 1E+030 7.1428571429
$C$12 VALUE Y 0 -12.5 40 12.5 1E+030
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$D$14 M1 CONST LHS 200 7.5 200 120 200
$D$15 M2 CONST LHS 250 0 400 1E+030 150
LET THE NUMBER OF CHAIRS BE X
LET THE NUMBER OF TABLES BE Y
MAX Z= 30X+40Y
STC: 4X + 7Y <= 200
5X + 5Y <= 400
X, Y >= 0
X Y MAX VALUE
COEFF 30 40
VALUE 50 0 1500
LHS SIGN RHS
M1 CONST 4 7 200 <= 200
M2 CONST 5 5 250 <= 400
PRODUCER SHOULD PRODUCE 50 CHAIRS AND 0 TABLES AND THE MAXIMUM PROFIT WILL BE Rs. 1500.
MACHINE 2 IS UNDERUTILIZED BY 150 Hrs. AND THE SHADOW PRICE FOR MACHINE 1 IS Rs. 7.5.
UM PROFIT WILL BE Rs. 1500.
MACHINE 1 IS Rs. 7.5.
Microsoft Excel 14.0 Answer Report
Worksheet: [LPP2.xlsx]QUES 4
Report Created: 10/16/2023 4:35:11 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 2 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
$E$12 VALUE MAX VALUE 0 668000
Variable Cells
Cell Name Original Value Final Value Integer
$B$12 VALUE X 0 12 Contin
$C$12 VALUE Y 0 0 Contin
$D$12 VALUE Z 0 124 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$E$14 LABOUR CONST LHS 1260 $E$14<=$G$14 Binding 0
$E$15 WOOD CONST LHS 2248 $E$15<=$G$15 Not Binding 16760
$E$16 SCREWS CONST LHS 396 $E$16<=$G$16 Binding 0
Microsoft Excel 14.0 Sensitivity Report
Worksheet: [LPP2.xlsx]QUES 4
Report Created: 10/16/2023 4:35:11 PM
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$12 VALUE X 12 0 4000 2666.6666667 666.66666667
$C$12 VALUE Y 0 -4111.1111111 2000 4111.1111111 1E+030
$D$12 VALUE Z 124 0 5000 1000 2000
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$E$14 LABOUR CONST LHS 1260 111.11111111 1260 1116 72
$E$15 WOOD CONST LHS 2248 0 19008 1E+030 16760
$E$16 SCREWS CONST LHS 396 1333.3333333 396 24 186
LET THE NUMBER OF TYPE 1 BOAT BE X
LET THE NUMBER OF TYPE 2 BOAT BE Y
LET THE NUMBER OF TYPE 3 BOAT BE Z
MAX Z = 4000X + 2000Y + 5000Z
STC: 12X + 7Y + 9Z <= 1260
22X + 18Y + 16Z <= 19008
2X + 4Y + 3Z <= 396
X Y Z MAX VALUE
COEFF 4000 2000 5000
VALUE 12 0 124 668000
LHS SIGN RHS
LABOUR C 12 7 9 1260 <= 1260
WOOD CON 22 18 16 2248 <= 19008
SCREWS C 2 4 3 396 <= 396
THE PRODUCER SHOULD PRODUCE 12 TYPE 1 BOATS, 0 TYPE 2 BOATS AND 124 TYPE 3 BOATS AND THE MAXIMUM
HERE WOOD IS UNDERUTILIZED BY 16760 (sq. feet) AND THE SHADOW PRICE FOR LABOUR IS 111.111111111111 A
3 BOATS AND THE MAXIMUM REVENUE GENERATED WILL BE EQUAL TO Rs. 668000.
BOUR IS 111.111111111111 AND FOR SCREWS IS 1333.33333333333.
