Warehouse
Plants Kansas City Louisville Supply Plants
Denvers 2 3 600 Denvers
Atlanta 3 1 400 Atlanta
Shipped
Plants
Warehouse Detroit Miami Dallas New Orleans Warehouse
Kansas City 2 6 3 6 Kansas City
Louisville 4 4 6 5 Louisville
Demand 200 150 350 300 Shipped
Demand
Total Cost
Warehouse
Kansas City Louisville Shipped Supply
550 50 600 600
0 400 400 400
550 450
Plants
Detroit Miami Dallas New Orleans Shipped
200 0 350 0 550
0 150 0 300 450
200 150 350 300
200 150 350 300
5200
Microsoft Excel 14.0 Answer Report
Worksheet: [Book2]Sheet1
Report Created: 12/3/2024 7:28:27 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 12 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
$I$15 Total Cost Detroit 0 5200
Variable Cells
Cell Name Original Value Final Value Integer
$I$3 Denvers Kansas City 0 550 Contin
$J$3 Denvers Louisville 0 50 Contin
$I$4 Atlanta Kansas City 0 0 Contin
$J$4 Atlanta Louisville 0 400 Contin
$I$10 Kansas City Detroit 0 200 Contin
$J$10 Kansas City Miami 0 0 Contin
$K$10 Kansas City Dallas 0 350 Contin
$L$10 Kansas City New Orleans 0 0 Contin
$I$11 Louisville Detroit 0 0 Contin
$J$11 Louisville Miami 0 150 Contin
$K$11 Louisville Dallas 0 0 Contin
$L$11 Louisville New Orleans 0 300 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$I$12 Shipped Detroit 200 $I$12=$I$13 Binding 0
$J$12 Shipped Miami 150 $J$12=$J$13 Binding 0
$K$12 Shipped Dallas 350 $K$12=$K$13 Binding 0
$L$12 Shipped New Orleans 300 $L$12=$L$13 Binding 0
$I$5 Shipped Kansas City 550 $I$5=$M$10 Binding 0
$J$5 Shipped Louisville 450 $J$5=$M$11 Binding 0
$K$3 Denvers Shipped 600 $K$3<=$L$3 Binding 0
$K$4 Atlanta Shipped 400 $K$4<=$L$4 Binding 0
Microsoft Excel 14.0 Sensitivity Report
Worksheet: [Book2]Sheet1
Report Created: 12/3/2024 7:28:28 AM
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$I$3 Denvers Kansas City 550 0 2 3 0
$J$3 Denvers Louisville 50 0 3 0 2
$I$4 Atlanta Kansas City 0 3 3 1E+030 3
$J$4 Atlanta Louisville 400 0 1 2 1E+030
$I$10 Kansas City Detroit 200 0 2 3 1E+030
$J$10 Kansas City Miami 0 1 6 1E+030 1
$K$10 Kansas City Dallas 350 0 3 4 1E+030
$L$10 Kansas City New Orleans 0 0 6 1E+030 0
$I$11 Louisville Detroit 0 3 4 1E+030 3
$J$11 Louisville Miami 150 0 4 1 1E+030
$K$11 Louisville Dallas 0 4 6 1E+030 4
$L$11 Louisville New Orleans 300 0 5 0 1E+030
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$I$12 Shipped Detroit 200 4 200 0 200
$J$12 Shipped Miami 150 7 150 0 50
$K$12 Shipped Dallas 350 5 350 0 350
$L$12 Shipped New Orleans 300 8 300 0 50
$I$5 Shipped Kansas City 550 2 0 0 550
$J$5 Shipped Louisville 450 3 0 0 50
$K$3 Denvers Shipped 600 0 600 1E+030 0
$K$4 Atlanta Shipped 400 -2 400 50 0
Microsoft Excel 14.0 Limits Report
Worksheet: [Book2]Sheet1
Report Created: 12/3/2024 7:28:28 AM
Objective
Cell Name Value
$I$15 Total Cost Detroit 5200
Variable Lower Objective Upper Objective
Cell Name Value Limit Result Limit Result
$I$3 Denvers Kansas City 550 550 5200 550 5200
$J$3 Denvers Louisville 50 50 5200 50 5200
$I$4 Atlanta Kansas City 0 0 5200 0 5200
$J$4 Atlanta Louisville 400 400 5200 400 5200
$I$10 Kansas City Detroit 200 200 5200 200 5200
$J$10 Kansas City Miami 0 0 5200 0 5200
$K$10 Kansas City Dallas 350 350 5200 350 5200
$L$10 Kansas City New Orleans 0 0 5200 0 5200
$I$11 Louisville Detroit 0 0 5200 0 5200
$J$11 Louisville Miami 150 150 5200 150 5200
$K$11 Louisville Dallas 0 0 5200 0 5200
$L$11 Louisville New Orleans 300 300 5200 300 5200
From To Shipped Unit Cost Node Outflow Inflow Netflow Sign
Plant1 WH1 550 2 Plant1 600 0 600 <=
Plant1 WH2 50 3 Plant2 400 0 400 <=
Plant2 WH1 0 3 WH1 550 550 0 =
Plant2 WH2 100 1 WH2 150 150 0 =
Plant2 O4 300 4 O1 0 200 -200 =
WH1 O1 200 2 O2 0 150 -150 =
WH1 O2 0 6 O3 0 350 -350 =
WH1 O3 350 3 O4 0 300 -300 =
WH1 O4 0 6
WH2 O1 0 4
WH2 O2 150 4
WH2 O3 0 6
WH2 O4 0 5
Total Cost 4600
Net Supply
600
400
0
0
-200
-150
-350
-300
Microsoft Excel 14.0 Answer Report
Worksheet: [Book2]Sheet3
Report Created: 12/3/2024 7:18:36 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.047 Seconds.
Iterations: 13 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
$D$1 Total Cost Unit Cost 4600 4600
Variable Cells
Cell Name Original Value Final Value Integer
$C$2 WH1 Shipped 550 550 Contin
$C$3 WH2 Shipped 50 50 Contin
$C$4 WH1 Shipped 0 0 Contin
$C$5 WH2 Shipped 100 100 Contin
$C$6 O4 Shipped 300 300 Contin
$C$7 O1 Shipped 200 200 Contin
$C$8 O2 Shipped 0 0 Contin
$C$9 O3 Shipped 350 350 Contin
$C$10O4 Shipped 0 0 Contin
$C$11O1 Shipped 0 0 Contin
$C$12O2 Shipped 150 150 Contin
$C$13O3 Shipped 0 0 Contin
$C$14O4 Shipped 0 0 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$I$2 Plant1 Netflow 600 $I$2<=$K$2 Binding 0
$I$3 Plant2 Netflow 400 $I$3<=$K$3 Binding 0
$I$4 WH1 Netflow 0 $I$4=$K$4 Binding 0
$I$5 WH2 Netflow 0 $I$5=$K$5 Binding 0
$I$6 O1 Netflow -200 $I$6=$K$6 Binding 0
$I$7 O2 Netflow -150 $I$7=$K$7 Binding 0
$I$8 O3 Netflow -350 $I$8=$K$8 Binding 0
$I$9 O4 Netflow -300 $I$9=$K$9 Binding 0
Microsoft Excel 14.0 Sensitivity Report
Worksheet: [Book2]Sheet3
Report Created: 12/3/2024 7:18:36 AM
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$C$2 WH1 Shipped 550 0 2 3 1
$C$3 WH2 Shipped 50 0 3 1 2
$C$4 WH1 Shipped 0 3 3 1E+030 3
$C$5 WH2 Shipped 100 0 1 2 2
$C$6 O4 Shipped 300 0 4 2 1E+030
$C$7 O1 Shipped 200 0 2 3 1E+030
$C$8 O2 Shipped 0 1 6 1E+030 1
$C$9 O3 Shipped 350 0 3 4 1E+030
$C$10 O4 Shipped 0 2 6 1E+030 2
$C$11 O1 Shipped 0 3 4 1E+030 3
$C$12 O2 Shipped 150 0 4 1 1E+030
$C$13 O3 Shipped 0 4 6 1E+030 4
$C$14 O4 Shipped 0 2 5 1E+030 2
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$I$2 Plant1 Netflow 600 0 600 1E+030 0
$I$3 Plant2 Netflow 400 -2 400 50 0
$I$4 WH1 Netflow 0 -2 0 550 0
$I$5 WH2 Netflow 0 -3 0 50 0
$I$6 O1 Netflow -200 -4 -200 200 0
$I$7 O2 Netflow -150 -7 -150 50 0
$I$8 O3 Netflow -350 -5 -350 350 0
$I$9 O4 Netflow -300 -6 -300 50 0
Microsoft Excel 14.0 Limits Report
Worksheet: [Book2]Sheet3
Report Created: 12/3/2024 7:18:36 AM
Objective
Cell Name Value
$D$17 Total Cost Unit Cost 4600
Variable Lower Objective Upper Objective
Cell Name Value Limit Result Limit Result
$C$2 WH1 Shipped 550 550 4600 550 4600
$C$3 WH2 Shipped 50 50 4600 50 4600
$C$4 WH1 Shipped 0 0 4600 0 4600
$C$5 WH2 Shipped 100 100 4600 100 4600
$C$6 O4 Shipped 300 300 4600 300 4600
$C$7 O1 Shipped 200 200 4600 200 4600
$C$8 O2 Shipped 0 0 4600 0 4600
$C$9 O3 Shipped 350 350 4600 350 4600
$C$10 O4 Shipped 0 0 4600 0 4600
$C$11 O1 Shipped 0 0 4600 0 4600
$C$12 O2 Shipped 150 150 4600 150 4600
$C$13 O3 Shipped 0 0 4600 0 4600
$C$14 O4 Shipped 0 0 4600 0 4600
