The computer solution for the linear program in Problem 1 provides the following
ID: 368284 • Letter: T
Question
The computer solution for the linear program in Problem 1 provides the following right-hand-side range information:
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___ to___ . As long as the right-hand side stays within this range, the dual value of 1.5 .
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 ___ for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is between ___ and .___
Variable RHS
Value Allowable
Increase Allowable
Decrease 1 10.00000 0.60000 3.00000 2 21.00000 9.00000 3.00000 3 16.00000 Infinite 1.50000
Explanation / Answer
1)
Upper limit of constraint 1 = RHS value + allowable increase = 10 + 0.6 = 10.6
Lower limit of constraint 1 = RHS value - allowable decrease = 10 - 3.0 = 7.0
The right-hand-side range for constraint 1 is 7 to 10.6 . As long as the right-hand side stays within this range, the dual value of 1.5 .
2)
Upper limit of constraint 2 = RHS value + allowable increase = 21 + 9 = 30
Lower limit of constraint 2 = RHS value - allowable decrease = 21 - 3 = 18
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 18 and 30
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