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Consider the following linear program:   Max 3A + 2B s.t.     1A + 1B ≤ 12   3A + 1B ≤ 26   1A + 2B ≤ 20     A, B ≥ 0   The value of the optimal solution is 31. Suppose that the right-hand side of the constraint 1 is increased from 12 to 13. Use the solution to part (a) to determine the dual value for constraint 1. If required, round your answer to 1 decimal place. Dual Value: 1.5 The computer solution for the linear program in Problem 1 provides the following right-hand-side range information:     Constraint   RHS Value   Allowable Increase   Allowable Decrease     1   12.00000   1.20000   3.33333     2   26.00000   10.00000   6.00000     3   20.00000   Infinite   3.00000   What does the right-hand-side range information for constraint 1 tell you about the dual value for constraint 1? If required, round your answers to five decimal places. The right-hand-side range for constraint 1 is 8.66667 to 13.200000. As long as the right-hand side stays within this range, the dual value is applicable.   . The dual value for constraint 2 is 0.5. Using this dual value and the right-hand-side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2? If required, round your answers to 1 decimal place. The improvement in the value of the optimal solution will be 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is between ________ and _________.

Consider the following linear program:   Max 3A + 2B s.t.     1A + 1B ≤ 12   3A + 1B ≤ 26   1A + 2B ≤ 20     A, B ≥ 0   The value of the optimal solution is 31. Suppose that the right-hand side of the constraint 1 is increased from 12 to 13. Use the solution to part (a) to determine the dual value for constraint 1. If required, round your answer to 1 decimal place. Dual Value: 1.5 The computer solution for the linear program in Problem 1 provides the following right-hand-side range information:     Constraint   RHS Value   Allowable Increase   Allowable Decrease     1   12.00000   1.20000   3.33333     2   26.00000   10.00000   6.00000     3   20.00000   Infinite   3.00000   What does the right-hand-side range information for constraint 1 tell you about the dual value for constraint 1? If required, round your answers to five decimal places. The right-hand-side range for constraint 1 is 8.66667 to 13.200000. As long as the right-hand side stays within this range, the dual value is applicable.   . The dual value for constraint 2 is 0.5. Using this dual value and the right-hand-side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2? If required, round your answers to 1 decimal place. The improvement in the value of the optimal solution will be 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is between ________ and _________.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 51P
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Consider the following linear program:

 

Max 3A + 2B
s.t.  
  1A + 1B ≤ 12
  3A + 1B ≤ 26
  1A + 2B ≤ 20
    A, B ≥ 0

 

The value of the optimal solution is 31. Suppose that the right-hand side of the constraint 1 is increased from 12 to 13.

  1. Use the solution to part (a) to determine the dual value for constraint 1. If required, round your answer to 1 decimal place.

    Dual Value: 1.5
  2. The computer solution for the linear program in Problem 1 provides the following right-hand-side range information:

       
    Constraint    		   RHS
    Value    		   Allowable
    Increase    		   Allowable
    Decrease    		  
      1   12.00000   1.20000   3.33333  
      2   26.00000   10.00000   6.00000  
      3   20.00000   Infinite   3.00000  

    What does the right-hand-side range information for constraint 1 tell you about the dual value for constraint 1? If required, round your answers to five decimal places.

    The right-hand-side range for constraint 1 is 8.66667 to 13.200000. As long as the right-hand side stays within this range, the dual value is applicable.
     
    .

  3. The dual value for constraint 2 is 0.5. Using this dual value and the right-hand-side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2? If required, round your answers to 1 decimal place.

    The improvement in the value of the optimal solution will be 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is between ________ and _________.

 

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