# Linear minimization problem

1. Dec 28, 2011

### specone

Hi all,

does anyone know what type of problem this would be classified as, and what kind of algorithm I could use to get a solution?

minimize:
P=60w1+30w2+10w3+100w4

subject to:
P ≥ 50
0 < wi ≤ 1

thanks very much

2. Dec 29, 2011

### mathman

What are you trying to minimize? Without this, the question is incomplete. Defining what you want to minimize with these conditions is called linear programing.

3. Dec 29, 2011

### AlephZero

It looks like a Linear Programming problem. The most straightforward solution algorithm is the Simplex Method.

4. Dec 30, 2011

### HallsofIvy

Staff Emeritus
The fundamental result in "linear programming" is that a minimum or maximum of a linear function, in a convex polyhedron, must occur at a vertex of the polhedron. Your condition, $0< w_i\le 1$, says that the "feasible region" is a n-dimensional rectangle and it is easy to calculate its $2^n$ vertices. However, the condition S> 50, on the target function will have to be applied after determining values. Also the fact that the faces $0= w_i$ are NOT in the feasible region can be a problem.