# In the simplex method, how is a pivot column selected? A pivot row? A pivot element? Give examples o

In

the simplex method, how is a pivot column selected? A pivot row? A pivot

element? Give examples of each.

True or False

1.

True or false. If all the

coefficients a1, a2, â€¦, an in

the objective function P = a1x1 + a2x2 +

â€¦ + anxn are nonpositive, then

the only solution of the problem is x1 = x2 =

â€¦ = xn and P = 0.

2.

True or false. The pivot column

of a simplex tableau identifies the variable whose value is to be decreased in

order to increase the value of the objective function (or at least keep it

unchanged).

3.

True or false. The ratio

associated with the pivot row tells us by how much the variable associated with

the pivot column can be increased while the corresponding point still lies in

the feasible set.

4.

True or false. At any

iteration of the simplex procedure, if it is not possible to compute the ratios

or the ratios are negative, then one can conclude that the linear programming

problem has no solution.

5.

True or false. If the last row to

the left of the vertical line of the final simplex tableau has a zero in a

column that is not a unit column, then the linear programming problem has

infinitely many solutions.

6.

True or false. Suppose you

are given a linear programming problem satisfying the conditions:

o The objective function is to be

minimized.

o All the variables involved are nonnegative,

and

o Each linear constraint may be written so that

the expression involving the variables is greater than or equal to a negative

constant.

Then

the problem can be solved using the simplex method to maximize the objective

function P = -C.

7.

True or false. The

objective function of the primal problem can attain an optimal value that is

different from the optimal value attained by the dual problem.

the simplex method, how is a pivot column selected? A pivot row? A pivot

element? Give examples of each.

True or False

1.

True or false. If all the

coefficients a1, a2, â€¦, an in

the objective function P = a1x1 + a2x2 +

â€¦ + anxn are nonpositive, then

the only solution of the problem is x1 = x2 =

â€¦ = xn and P = 0.

2.

True or false. The pivot column

of a simplex tableau identifies the variable whose value is to be decreased in

order to increase the value of the objective function (or at least keep it

unchanged).

3.

True or false. The ratio

associated with the pivot row tells us by how much the variable associated with

the pivot column can be increased while the corresponding point still lies in

the feasible set.

4.

True or false. At any

iteration of the simplex procedure, if it is not possible to compute the ratios

or the ratios are negative, then one can conclude that the linear programming

problem has no solution.

5.

True or false. If the last row to

the left of the vertical line of the final simplex tableau has a zero in a

column that is not a unit column, then the linear programming problem has

infinitely many solutions.

6.

True or false. Suppose you

are given a linear programming problem satisfying the conditions:

o The objective function is to be

minimized.

o All the variables involved are nonnegative,

and

o Each linear constraint may be written so that

the expression involving the variables is greater than or equal to a negative

constant.

Then

the problem can be solved using the simplex method to maximize the objective

function P = -C.

7.

True or false. The

objective function of the primal problem can attain an optimal value that is

different from the optimal value attained by the dual problem.