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

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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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 _________.

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