Consider Theorem 1.7 in the text as applied to the following general linear prog

Question

Consider Theorem 1.7 in the text as applied to the following general linear programming problem: Find values (x, y) element R2 that minimize z = x subject to the constraint x greaterthanorequalto 20. Is the feasible set ((x, y) element R2: x greaterthanorequalto 0) nonempty and unbounded? What is the optimal (i.e. minimal) value of z in this feasible set? Does an optimal solution exist, i.e. does there exist a feasible point (x, y) which attains the optimal value for x? Does the feasible set have any extreme points? What does Theorem 1.7 assert as applied to this example? How does that compare to your answers above? What conclusion do you draw from this? Let S be the set of feasible solutions to a general linear programming problem. If S is nonempty and bounded, then an optimal solution to the problem exists and occurs at an extreme point. If S is nonempty and not bounded and if an optimal solution to the problem exists, then an optimal solution occurs at an extreme point. If an optimal solution to the problem does not exist, then either S is empty or S is unbounded.

Explanation / Answer

{(0,y): y in R} is the required set.

(a) non empty and unbounded.

(b) zero

(c) yes there exists infinitely many in fact uncountable all on y-axis

(D) yes

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