# Linear programming help

• May 13th 2009, 12:30 PM
thequalicum
Linear programming help
Hi, I need some help with these questions. Thanks!
Here are the problems:
1. Put the following LP problem in standard form.
minmize z = 2x(1) + 4X(2) subject to
x(1) + x(3) [greaterorequalto] 4
x(2) + x(3) = 1
x(2), x(3) [greaterorequalto] 0
x(1) unconstrained

I know what to do with the first 3 constraints but what do I do with the x(1) unconstrained variable?

2. Maximize z = 40x(1) + 60x(2) subject to
2(x1) + x(2) [less than or equa lto] 7
x(1) + x(2) [less than or equal to] 4
x(1) + 3x(2) [less than or equal to] 9
x(1), x(2) [greater or equal to] 0

Solve the LP problem using the "corner point" method. Clearly state the optimal value and optimal function.
• May 16th 2009, 01:31 AM
CaptainBlack
Quote:

Originally Posted by thequalicum
Hi, I need some help with these questions. Thanks!
Here are the problems:
1. Put the following LP problem in standard form.
minmize z = 2x(1) + 4X(2) subject to
x(1) + x(3) [greaterorequalto] 4
x(2) + x(3) = 1
x(2), x(3) [greaterorequalto] 0
x(1) unconstrained

I know what to do with the first 3 constraints but what do I do with the x(1) unconstrained variable?

You don't do anything with it, its not a constraint.

(also note that x(3) is a thinly disquised slack variable used to convert an inequality constraint to equality constraint)

CB