1. (25 pt) True or false: () The original problem has a feasible solution if and
ID: 3210388 • Letter: 1
Question
1. (25 pt) True or false: () The original problem has a feasible solution if and only if the optimal value of the auxiliary problem is zero.) (b) The simplex methods terminates as long as there is no leaving variable )The LP problem is unbounded if there is a 'bad' column in the tableau, ie. all elements in that column are nonpositive ) (d) The audliary objective function is not always bounded) (e) I both the max and min problems have feasible solutions, then both objective functions have optimal solutions and same optimal value.Explanation / Answer
a) true , the original problem has a feasible solution if the auxilairy problem 1111has optimal solution x0 =0 , If the LP has no optimal origin we first solve the auxialiary proble, then the original prob1lem as second phase.
b)FAlse, A simplex algorithm terminates as long as the choice of variable to enter or leave the basis is made according to the smallest subscript rule
c) True , The Lp problem is unbounded if the feasible region is unbounded,that means unboundedness can be detected when we encountered a pivot column that does not contain any positive entry
d)False, Auxialiary Objective function is always bounded
e)True, If a feasible region of a LPP is non empty and bounded , then both min and max has fesible solution and attains the feasible solution at some extrme points , thus may have same values
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