Consider the solution of the following linear programming problem Use the output shown below to answer the following questions LINEAR PROGRAMMING PROBLEM MAX 25X1 30X2 15X3 S T 1) 4X1 5X2 8X3 1200 2) 9X1 15X2 3X3 1500 OPTIMAL SOLUTION Objective Function Value 4700 000 Variable Value Reduced Cost X1 140 000 0 000 X2 0 000 10 000 X3 80 000 0 000 Constraint Slack Surplus Dual Price 1 0 000 1 000 2 0 000 2 333 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 19 286 25 000 45 000 X2 No Lower Limit 30 000 40 000 X3 8 333 15 000 50 000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 666 667 1200 000 4000 000 2 450 000 1500 000 2700 000 (4 points)Determine the slack of constraint 1 Is constraint 1 a binding constraint Why or why not (3 points) Notice that the current value of X2 in the optimal solution is 0 If the coefficient of X2 in the objective function is increased to 45 and the problem is re solved, will the value of X2 at optimality be impacted Why or why not (8 points) If the objective function coefficient of all variables simultaneously increase by 5 units each, would the current solution still remain optimal Will the objective function value be impacted at all Explain your answer (5 points) All else remaining the same, what action would you recommend so that X2 becomes positive at optimality Explain your answer

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Consider the solution of the following linear programming problem. Use the output shown below to answer the following questions. LINEAR PROGRAMMING PROBLEM MAX 25X1+30X2+15X3 S.T.

Consider the solution of the following linear programming problem. Use the output shown below to answer the following questions.

LINEAR PROGRAMMING PROBLEM MAX 25X1+30X2+15X3 S.T. 1) 4X1+5X2+8X3<1200 2) 9X1+15X2+3X3<1500 OPTIMAL SOLUTION Objective Function Value = 4700.000 Variable Value Reduced Cost X1 140.000 0.000 X2 0.000 10.000 X3 80.000 0.000 Constraint Slack/Surplus Dual Price 1 0.000 1.000 2 0.000 2.333 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 19.286 25.000 45.000 X2 No Lower Limit 30.000 40.000 X3 8.333 15.000 50.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 666.667 1200.000 4000.000 2 450.000 1500.000 2700.000

(4 points)Determine the slack of constraint1.Is constraint 1 a binding constraint? Why or why not?
(3 points) Notice that the current value of X2 in the optimal solution is 0. If the coefficient of X2 in the objective function is increased to 45 and the problem is re-solved, will the value of X2 at optimality be impacted? Why or why not?
(8 points) If the objective function coefficient of all variablessimultaneouslyincrease by 5 units each, would the current solution still remain optimal? Will the objective function value be impacted at all? Explain your answer.
(5 points) All else remaining the same, what action would you recommend so that X2 becomes positive at optimality? Explain your answer.