please answer # 4 , 5 and 6 !!! LP problem (see the feas ible region in Figure 1

Question

please answer # 4 , 5 and 6 !!!

LP problem (see the feas ible region in Figure 1) Max ztx1-x23-5x1 + 4x2 x2 S.t 24 Constraint 1) 6 Constraint 2) 1 Constraint 3) 2 (Constraint 4) 0 (Constraint 5) Constraint 6) 6x1 4x2 x12x2 ·x1 + x2 x1 01. What is the slope of the Objective function? 1, 2) slope is- gz. What is the optimal value zix1, x2)? 03. What is the slope of each of the constraints? Constraint 1 slope Constraint 2 slope- Constraint 3 slope- Constraint 4 slope - 04. Which are the optimal binding constraints? YES or NO Constraint 1: YES NO Constraint 2: YES NO Constraint 3: YES NO Constraint 4: YES NO Constraint 5: YES NO Constraint 6 YES NO Q5. Find the slack value for each constraint constraint 1:51 Figure 1. LP Problem Constraint Region Constraint 2:s2 Constraint 3: s3 constraint 4:54 Q6. what Objective functions wi·eve us multiple (alternative) optima where stil the original optimum value stays the same? Objective Function 1: Objective Function 2: Objective Function 3:

Explanation / Answer

4>A bindiing copnstraint is a cosntarint whose slack values is zero

constraint1 no constarint2 no constraint3 yes constraint 4 no constraint 5 yes constraint 6 yes

optimla soultion x1= x2=1.

5>slack value constraint1: optimal solution 4 slack :20 constraint2 : slack value:4 constraint 3: slack value:nil

6> All the functions contribute to the optimal solution

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