Formulation for Simplex Method:
Variables : F = Full time students
P1= Part time attending 3 days
P2 = Part time attending 2 days
Objective Function : Max Z = 650*F + 460*P1 + 350*P2
Constraints : F + P2<= 50
F + P1<= 50
We introduce non-negative, slack variables S1 and S2 and formulate the problem as follows:
Maximize Z = 650 F + 460 P1 + 350 P2
subject to : F + P1 + S1 = 50
F + P2 + S2 = 50
F, P1, P2, S1, S2 >= 0
We then have an initial basic feasible solution (F, P1, P2, S1, S2) =
(0,0,0,50,50). S1 and S2 are the basic variables and F, P1, and P2 are
the nonbasic variables.
We note that the coefficients on the nonbasic variables in the expression
for Z are positive so that we may choose any of the nonbasics to be the
entering basic variable in the simplex method. (In general any nonbasic
with a positive coefficient in the objective may be chosen as an entering ...
This shows how to use the simplex method to maximize an objective function with given constraints.