This would normally be written as x1 > 1. Did you mean x1 + 2x2 > 3?bobbo7410 said:Homework Statement
I don't exactly have a specific example, I'm looking for the general idea behind LP constraints.
Homework Equations
Within the constraints, do the variables have to be all to one side?
For instance, X1 + 2 > 3 is a standard constraint
No. This is equivalent to 2 > 1, which is always true, so doesn't constrain things in any way. Did you mean x1 + 2 > x2 + 1?bobbo7410 said:would for example
X1 + 2 > X1 + 1
still be acceptable as a constraint?
Mark44 said:You can always move variables from one side of an equation/inequality to the other.
Mark44 said:To use matrix methods (e.g., Simplex tableau), you need to have all the variables on one side, and the constant on the other. I'm pretty sure this is correct, although I haven't done one of these problems for a good long while.
The main purpose of formulating an LP (Linear Programming) problem is to find the optimal solution to a real-world problem. This involves maximizing or minimizing a linear objective function while satisfying a set of linear constraints.
The steps for formulating an LP problem are as follows: 1. Define the decision variables2. Write the objective function3. Write the constraints4. Identify any additional conditions or restrictions5. Convert the problem into standard form (if necessary)
A decision variable is a quantity that the decision maker can control or change in order to achieve the desired outcome. On the other hand, a constraint is a limitation or restriction on the decision variables that must be satisfied in order to find a feasible solution to the problem.
An LP problem has a feasible solution if there exists at least one combination of decision variable values that satisfies all of the constraints. This can be determined by graphing the constraints and finding the feasible region, or by using a computer program to solve the problem.
LP problems have a wide range of applications in different fields, including engineering, economics, transportation, and resource allocation. Some examples of real-world applications include production planning, portfolio optimization, diet planning, and scheduling.