Solving a Nonstandard Problem
a. If necessary, convert the problem to a maximization problem.
b. Add slack variable and subtract surplus variables as needed.
c. Write the initial simplex tableau.
d. If any basic variable has a negative value, locate the nonzero number in the variable’s column, and note what row it is in.
e. In the row located in Step d, find the positive entry that is farthest to the left, and note what column it is in.
f. In the column found in Step e. Choose a pivot by investigating quotients.
g. Use row operation to change the other number in the pivot column to 0.
h. Continue Steps d through g until all basic variables are nonnegative. If it ever becomes impossible to continue, then the problem has no feasible solution.
i. Once a feasible solution has been found, continue to use the simplex method until the optimal solution is found.