Using the following solution LINEAR PROGRAMMING PROBLEM MAX 100X1 120X2 150X3 125X4 S T 1) 1X1 2X2 2X3 2X4 108 2) 3X1 5X2 1X4 120 3) 1X1 1X3 25 4) 1X2 1X3 1X4 50 OPTIMAL SOLUTION Objective Function Value 7475 000 Variable Value Reduced Costs X1 8 000 0 000 X2 0 000 5 000 X3 17 000 0 000 X4 33 000 0 000 Constraint Slack Surplus Dual Prices 1 0 000 75 000 2 63 000 0 000 3 0 000 25 000 4 0 000 25 000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 87 500 100 000 No Upper Limit X2 No Lower Limit 120 000 125 000 X3 125 000 150 000 162 500 X4 120 000 125 000 150 000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 100 000 108 000 123 750 2 57 000 120 000 No Upper Limit 3 8 000 25 000 58 000 4 41 500 50 000 54 000 To answer the following questions What is the optimal solution and optimal value Which constraints are binding and non binding and what are there slack or surplus values Please type your answer below What does the Objective Coefficient Ranges mean and what are they for the first and third variables Could the profit for X 2 increase by 10 and how does the reduced cost information add to this analysis Can the profit of X 2 increase by 50 and how does the Reduced Cost help with this decision Explain Please type your answer below Apply the 100 Rule to the Objective Coefficient Ranges How do these changes impact the optimal value for the problem Please type your answer below What does Dual Price mean and what are they for each constraint Which constraint represents the most valuable resource For your chosen most important resource, what is the allowable increase to the right hand side and what would the new profit be Please type your answer below What does the Right Hand Side Ranges mean and what are they for the first and third constraints In addition, is it possible to decrease the right hand side of the second constraint by 50 What is the effect on the optimal value if this change is made Please type your answer below F) Apply the 100 Rule to the Right hand side ranges How do these changes impact the optimal value for the problem

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Using the following solution: LINEAR PROGRAMMING PROBLEM MAX 100X1+120X2+150X3+125X4 S.T. 1) 1X1+2X2+2X3+2X4 <108 2) 3X1+5X2+1X4 <120 3) 1X1+1X3 <25 4) 1X2+1X3+1X4>50 OPTIMAL SOLUTION Objective Function

Using the following solution:

LINEAR PROGRAMMING PROBLEM

MAX 100X1+120X2+150X3+125X4

S.T.

1) 1X1+2X2+2X3+2X4<108

2) 3X1+5X2+1X4<120

3) 1X1+1X3<25

4) 1X2+1X3+1X4>50

OPTIMAL SOLUTION

Objective Function Value = 7475.000

Variable Value Reduced Costs

-------------- --------------- ------------------

X1 8.000 0.000

X2 0.000 5.000

X3 17.000 0.000

X4 33.000 0.000

Constraint Slack/Surplus Dual Prices

-------------- --------------- ------------------

1 0.000 75.000

2 63.000 0.000

3 0.000 25.000

4 0.000 -25.000

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

------------ --------------- --------------- ---------------

X1 87.500 100.000 No Upper Limit

X2 No Lower Limit 120.000 125.000

X3 125.000 150.000 162.500

X4 120.000 125.000 150.000

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit

------------ --------------- --------------- ---------------

1 100.000 108.000 123.750

2 57.000 120.000 No Upper Limit

3 8.000 25.000 58.000

4 41.500 50.000 54.000

To answer the following questions.

What is the optimal solution and optimal value? Which constraints are binding and non-binding and what are there slack or surplus values? Please type your answer below.

What does the Objective Coefficient Ranges mean..and what are they for the first and third variables? Could the profit for X₂ increase by 10% and how does the reduced cost information add to this analysis? Can the profit of X₂ increase by 50% and how does the Reduced Cost help with this decision? Explain.

Please type your answer below.

Apply the 100% Rule to the Objective Coefficient Ranges. How do these changes impact the optimal value for the problem?

Please type your answer below.

What does Dual Price mean and what are they for each constraint? Which constraint represents the most valuable resource? For your chosen most important resource, what is the allowable % increase to the right-hand side and what would the new profit be?

Please type your answer below.

What does the Right Hand Side Ranges mean.and what are they for the first and third constraints. In addition, is it possible to decrease the right-hand side of the second constraint by 50%? What is the effect on the optimal value if this change is made?

Please type your answer below.

F) Apply the 100% Rule to the Right hand-side ranges. How do these changes impact the optimal value for the problem?