points) For each part below, determine whether the given assertion is TRUE or FA
ID: 3184799 • Letter: P
Question
points) For each part below, determine whether the given assertion is TRUE or FALSE. No justification is required. Circle your answer. (a) (1 point) Let be a vertex of the feasible region of a max LP. If there are no adjacent vertices with a larger z-value than z(x), then z is the optimal solution to the LP. TRUE or FALSE (b) (1 point) Let z be an objective function defined on a feasible region R. Then min z(x) = _ max[-2(x)]. TRUE or FALSE (c) (1 point) Let z be a linear objective function defined on a feasible region R, and let axk(x)+8 = b+max z(x) and min[2(x)+b] = b+min z (x). b be a constant. Then m rER TRUE or FALSE (d) (1 point) The set of optimal solutions to an LP is a convex set. TRUE or FALSE (e) (1 point) If a nonbasic variable has coefficient 0 in row zero of the optimal tableau, then the LP has alternative optimal solutions. TRUE or FALSEExplanation / Answer
a. TRUE, since An optimal solution to a linear program is the feasible solution with the largest objective function value (for a maximization problem).
b.FALSE,since min[z(x)]= -max[z(x)]
c.TRUE,since min[z(x)+b]=min[z(x)]+b if b is constant then it will not change and also same for the maximization also
d.TRUE,since If an LP has a finite optimum then there is an optimal basic feasible solution and Basic feasible solutions extreme points of the feasible set and The feasible set of an LP problem is convex.
e.FALSE,since in first tableau the non basic variables are the variables of z whose cofficients cant be zero.if it is so then we do not get any solution.
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