This is to continue the example introducing slack
and surplus variables. The reformulated model was written into the initial
The initial basic solution consists of the slack variables
solution variables, and variables,
and as outside
variables. This is not a very profitable solution, with profit P = 0. It
calls for no production of either product A or B. The terms
entered in the simplex table under the "Solution variables" column, and
their per-unit profits (the cj) are entered in the first line.
The solution variables can be identified as those having columns under
them containing one element with +1, and the remainder of the elements
0. Also, the 1 must be in a different row than the 1 of any other column.
a 1 in the first row, and has
a 1 in the second row. Note that this is equivalent to saying that we have
solved the constraint equations in terms of and :
The variables omitted from the solution are currently, and ;
they are equal to 0. Thus, for this first trial solution, =
Note that we have a diagonal of 1s, and the remainder
of the numbers in the n columns are zeros.