Consider a linear programming problem in standard form and assume that the rows of a are linearly independent. for each one of the following statements, provide either a proof or a counterexample. (a) let x* be a basic feasible solution. suppose that for every basis corresponding to x* , the associated basic solution to the dual is infeasible. then, the optimal cost must be strictly less that c' x* .

if im undersanding the question correctly, its organized from 10

step-by-step explanation:

6hryt%4578855

part a: 1.08

part b: 27.59

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)