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, …, an in
the objective function P = a1x1 + a2x2 +
… + anxn are nonpositive, then
the only solution of the problem is x1 = x2 =
… = 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.