a. What would happen to dual price values if the right-hand side of constraint 1 increased by 1, right hand- side of constrain 2 decreased by 5 and right-hand side of constraint 3 increased by 5 units simultaneously? What is the new optimal objective function value?

 b. Which constraints are binding?

c. What would happen to the optimal solution if the coefficient of X2 increased by 2 and coefficient of X3 decrease by 2? What is the new optimal value?

d. Which constrain(s) have surplus variable(s)?

e. What is the dual problem?

f. Use the dual prices and constraints to show the objective function value is optimal?

Transcribed Image Text:

MAX S.T. X₂ X₁ X₁ Variable X₁ 100X₁+120X₂+150X3+125X4 OPTIMAL SOLUTION Objective Function Value = 7475.000 2 3 1) X₁ + 2X₂+2X₁ + 2X4 ≤ 108 2) 3X₁ +5X₂+ X4S 120 3) X₁ 4) Constraint X3 X4 Variable X₁ X₂ + X₂ X₂+ X₁ + X₁X₂X₁, X20 234 Constraint 1 2 Value 8.000 0.000 17.000 33.000 ≤25 X₁2 50 Slack/Surplus 0.000 63.000 0.000 0.000 OBJECTIVE COEFFICIENT RANGES RIGHT HAND SIDE RANGES Lower Limit 100.000 57.000 8.000 41.500 Reduced Cost 0.000 5.000 0.000 0.000 Lower Limit 87.500 No Lower Limit 125.000 120.000 Dual Price 75.000 0.000 25.000 -25.000 Current Value 100.000 120.000 150,000 125.000 Current Value 108.000 120.000 25.000 50.000 Upper Limit No Upper Limit 125.000 162.500 150.000 Upper Limit 123.750 No Upper Limit 58.000 54.000 MAX S.T. X₂ X₁ X₁ Variable X₁ 100X₁+120X₂+150X3+125X4 OPTIMAL SOLUTION Objective Function Value = 7475.000 2 3 1) X₁ + 2X₂+2X₁ + 2X4 ≤ 108 2) 3X₁ +5X₂+ X4S 120 3) X₁ 4) Constraint X3 X4 Variable X₁ X₂ + X₂ X₂+ X₁ + X₁X₂X₁, X20 234 Constraint 1 2 Value 8.000 0.000 17.000 33.000 ≤25 X₁2 50 Slack/Surplus 0.000 63.000 0.000 0.000 OBJECTIVE COEFFICIENT RANGES RIGHT HAND SIDE RANGES Lower Limit 100.000 57.000 8.000 41.500 Reduced Cost 0.000 5.000 0.000 0.000 Lower Limit 87.500 No Lower Limit 125.000 120.000 Dual Price 75.000 0.000 25.000 -25.000 Current Value 100.000 120.000 150,000 125.000 Current Value 108.000 120.000 25.000 50.000 Upper Limit No Upper Limit 125.000 162.500 150.000 Upper Limit 123.750 No Upper Limit 58.000 54.000

Answer rating: 100% (QA)

Given the provided information lets address each of the questions a To determine the new dual price values and the new optimal objective function value when the righthand side RHS values of constraints change you need to look at the dual prices and the RHS ranges Here the dual price also known as the shadow price represents the change in the objective function value per unit increase in the RHS of the constraint ... View the full answer