Question

Find the complete optimal solution to this linear programming problem (using Excel) and enter the optimal x value.

Max 5X + 6Y

s.t. 3X + Y <= 15

X + 2Y <= 12

3X + 2Y <= 24

X , Y >= 0

Find the complete optimal solution to this linear programming problem using Excel and type in the optimal value of X below (X*=?).

Max 2X + 3Y

s.t. 4X + 9Y <= 72

10X + 11Y <= 110

17X + 9Y <= 153

X , Y >= 0

Answer 1

Get External Data Connections Solver Parameters Set Objective: ES SBS3 X B3 A C D To: 0 OValue Of: Min Max 1 x Y By Changing Variable Cells: 2 SAS2:SBS2 3 5x+6y 4 3x+y 0 Subject to the Constraints: 5x+2y 0 SBS4 15 SBS5 <12 SB$6 24 Add 6 3x+2y 7 Change 8 91 Delete 10 11 Reset All 12 13 Load/Save 14 Make Unconstrained Variables Non-Negative 15 Select a Solving Method: GRG Nonlinear Options 16 17 Solving Method 18 Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP 19 Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. 20 21 22 Solve Help Close Sheet8 Cayley table Sheet6 Sheet3 X n

And the solution:

B7 Solver Results X B A D F Solver found a solution. All Constraints and optimality conditions are satisfied 1 X Reports 2 3.6 4.2 Answer 3 5x+бу 4 3x+y 5 x+2y 6 3x+2y Keep Solver Solution 43.2 Sensitivity Limits 15 Restore Original Values 12 19.2 Return to Solver Parameters Dialog Outline Reports Save Scenario... OK Cancel 9 10 Solver found a solution. All Constraints and optimality conditions are satisfied 11 12 When the GRG engine is used, Solver has found at least a local optimal solution. When Simplex LP is used, this means Solver has found a global optimal solution 13 14 15 . LO N

So that $(x,y)=(3.6,4.2)$ is the optimal point and optimal value is $43.2$