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2) Consider the following two linear programs, where x, c E R"; y,b E Rm; A e RM×n . [LP1] max c"x [LP2] min b"y y х s.t. ΑXb s.t. A" y > c x 2 0 y > 0 Which of the following statements is/ are correct? A. If [LP1] has a feasible solution, then [LP2] must have a feasible solution. B. Let x be a feasible solution to [LP1] and y be a feasible solution to [LP2]. Then we must have c"x = b" y. C. If [LP1] is infeasible, then [LP2] must also be infeasible. D. If [LP2] is unbounded, then [LP1] must also be unbounded. E. The dual of [LP 1] is [LP 2], and the dual of [LP 2] is [LP 1].

2) Consider the following two linear programs, where x, c E R"; y,b E Rm; A e RM×n . [LP1] max c"x [LP2] min b"y y х s.t. ΑXb s.t. A" y > c x 2 0 y > 0 Which of the following statements is/ are correct? A. If [LP1] has a feasible solution, then [LP2] must have a feasible solution. B. Let x be a feasible solution to [LP1] and y be a feasible solution to [LP2]. Then we must have c"x = b" y. C. If [LP1] is infeasible, then [LP2] must also be infeasible. D. If [LP2] is unbounded, then [LP1] must also be unbounded. E. The dual of [LP 1] is [LP 2], and the dual of [LP 2] is [LP 1].

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3BEXP
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2) Consider the following two linear programs, where x, c E R"; y,b e R™; A E R™×n . [LP1] max c' x [LP2] min b'y у s.t. Ах < b s.t. A" y 2 c x > 0 y 2 0 Which of the following statements is/ are correct? A. If [LP1] has a feasible solution, then [LP2] must have a feasible solution. B. Let x be a feasible solution to [LP1] and y be a feasible solution to [LP2]. Then we must have c"x = b" y. C. If [LP1] is infeasible, then [LP2] must also be infeasible. D. If [LP2] is unbounded, then [LP1] must also be unbounded. E. The dual of [LP 1] is [LP 2], and the dual of [LP 2] is [LP 1].
Transcribed Image Text:2) Consider the following two linear programs, where x, c E R"; y,b e R™; A E R™×n . [LP1] max c' x [LP2] min b'y у s.t. Ах < b s.t. A" y 2 c x > 0 y 2 0 Which of the following statements is/ are correct? A. If [LP1] has a feasible solution, then [LP2] must have a feasible solution. B. Let x be a feasible solution to [LP1] and y be a feasible solution to [LP2]. Then we must have c"x = b" y. C. If [LP1] is infeasible, then [LP2] must also be infeasible. D. If [LP2] is unbounded, then [LP1] must also be unbounded. E. The dual of [LP 1] is [LP 2], and the dual of [LP 2] is [LP 1].
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