Chapter 4.11, Problem 3P

Explanation of Solution

Linear Programming Problem

• ${\text{x}}_{\text{1}}$, ${\text{x}}_{\text{2}}$, ${\text{x}}_{\text{3}}$, ${\text{x}}_{\text{4}}$, ${\text{s}}_{\text{1}}$ and ${\text{s}}_{\text{2}}$ are the basic variables.
• For solving a linear problem using simplex algorithm, first the linear problem is converted to its standard form.
• Then a basic feasible solution is found which is easy if all the constraints are less than or equal with non-negative right hand side.
• If all nonbasic variables have nonnegative coefficients in row 0 then that basic feasible solution is optimal.
• If any variable have negative coefficient in row 0 then the variable with the most negative coefficient is chosen to enter the basis.
• If one or more constraints have a negative right hand side then there is no longer a basic feasible solution.
• After first iteration, the initial table is

z	x1	x2	x3	x4	s1	s2	RHS
1	-2	-3	1	12	0	0	0
0	-2	-9	1	9	1	0	0
0	1/3	1	-1/3	-2	0	1	0

• Afte