Class_7_LP_Slides

# Greater or equal to input the left hand side and

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greater or equal to Input the left-hand side and right-hand side of the equality (or inequality) Each row is one constraint Select nonnegative variable if ALL variables are nonnegative in nature. Constraints 2013 43 QSO 510 Solver in Excel

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Wilson Manufacturing Variables Baseballs Softballs Dozens 100 200 Objective Baseballs Softballs Total Profit Unit Profit \$7.00 \$10.00 =B7*B4+C7*C4 Constraints Baseballs Softballs Total Limits Cowhide 5 6 =B10*B4+C10*C4 <= 3600 Production time 1 2 =B11*B4+C11*C4 <= 960 Capacity Baseball =B4 <= 500 Capacity Softball =C4 <= 500 Wilson Manufacturing Example 2013 44 QSO 510 Solver in Excel
Objective Final optimal result Variable Optimal decisions Constraints Whether a condition is binding or non-binding at optimal. What’s the effect of changing a parameter? Objective coefficient Constraint limit Answer Report Sensitivity Report 2013 45 QSO 510 Interpret Solver Results

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2013 46 QSO 510 Answer Report Objective Cell (Max) Cell Name Original Value Final Value \$D\$7 Unit Profit Total Profit 5,520.00 \$ 5,520.00 \$ Variable Cells Cell Name Original Value Final Value Integer \$B\$4 Dozens Baseballs 360 360 Contin \$C\$4 Dozens Softballs 300 300 Contin Constraints Cell Name Cell Value Formula Status Slack \$D\$10:\$D\$13 <= \$F\$10:\$F\$13 \$D\$10 Cowhide Total 3600 \$D\$10<=\$F\$10 Binding 0 \$D\$11 Production time Total 960 \$D\$11<=\$F\$11 Binding 0 \$D\$12 Capacity Baseball Total 360 \$D\$12<=\$F\$12 Not Binding 140 \$D\$13 Capacity Softball Total 300 \$D\$13<=\$F\$13 Not Binding 200
Sensitivity Report What’s the effect of changing a parameter? Objective coefficient Constraint limit 2013 QSO 510 47 Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease \$B\$4 Dozens Baseballs 360 0 7 1.333333333 2 \$C\$4 Dozens Softballs 300 0 10 4 1.6 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease \$D\$10 Cowhide Total 3600 1 3600 280 720 \$D\$11 Production time Total 960 2 960 160 93.33333333 \$D\$12 Capacity Baseball Total 360 0 500 1E+30 140 \$D\$13 Capacity Softball Total 300 0 500 1E+30 200

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What’s effect of changing the objective function coefficient? When will the optimal solution remain the same? The optimal decisions remain the same when Coefficient for baseball is Coefficient for softball is Objective Function 2013 48 QSO 510 Sensitivity Report Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease \$B\$4 Dozens Baseballs 360 0 7 1.333333333 2 \$C\$4 Dozens Softballs 300 0 10 4 1.6
Changing the limit of nonbinding constraints produces no effect Optimal decisions remain the same.; Shadow price for that resource is 0; Remains no effect when the limit is Baseball capacity Softball capacity 2013 49 QSO 510 Sensitivity Report—Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease \$D\$10:\$D\$13 <= \$F\$10:\$F\$13 \$D\$10 Cowhide Total 3600 1 3600 280 720 \$D\$11 Production time Total 960 2 960 160 93.33333333 \$D\$12 Capacity Baseball Total 360 0 500 1E+30 140 \$D\$13 Capacity Softball Total 300 0 500 1E+30 200

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Changing the limit of binding constraints produces effect Optimal decisions change;

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