# Linear Programming, simplex method

• February 8th 2010, 11:40 AM
the prince
Linear Programming, simplex method
hi!(Hi)
i have trouble with the simplex method, i know how to solve if there is for example <= in the system but i don't know if there is only = because i don't know wich variable to take as basic variable (ex. x_11= 5- x_12)
x_11 + x_12=5
x_21 + x_22=7
x_11 + x_21=4
x_12 + x_22=8

x_ij>= 0 ,i=(1,2) ; j=(1,2)

min z=x_11+2x_12+2x_21+3x_22

i would be really thankful if someone can help me beacuse i have tomorrow a test (Worried)
• February 8th 2010, 07:05 PM
kjchauhan
Quote:

Originally Posted by the prince
hi!(Hi)
i have trouble with the simplex method, i know how to solve if there is for example <= in the system but i don't know if there is only = because i don't know wich variable to take as basic variable (ex. x_11= 5- x_12)
x_11 + x_12=5
x_21 + x_22=7
x_11 + x_21=4
x_12 + x_22=8

x_ij>= 0 ,i=(1,2) ; j=(1,2)

min z=x_11+2x_12+2x_21+3x_22

i would be really thankful if someone can help me beacuse i have tomorrow a test (Worried)

Note that,

$x_{11} + x_{12}=5$

is equivalent to

$x_{11} + x_{12} \le 5$

$-x_{11} - x_{12} \le -5$

So, I think u get it.. Best luck.