Question

This may be quite a basic question for someone who knows linear programming.
In most of the problems that I saw on LP has somewhat similar to following format

max            3x+4y  
subject to     4x-5y = -34
               3x-5y = 10      (and similar other constraints)

So in other words, we have same number of unknown in objective and constraint functions.

My problem is that I have one unknown variable in objective function and 3 unknowns in constraint functions.
The problem is like this

Objective function:  min w1
subject to:
w1 + 0.1676x + 0.1692y >= 0.1666 
w1 - 0.1676x - 0.1692y >= -0.1666 
w1 + 0.3039x + 0.3058y >= 0.3  
w1 - 0.3039x - 0.3058y >= -0.3  
x + y = 1
x >= 0
y >= 0

As can be seen, the objective function has only one unknown i.e. w1 and constraint functions have 3 (or lets say 2) unknown i.e w1, x and y.
Can somebody please guide me how to solve this problem, especially using R or MATLAB linear programming toolbox.

Answer 1

Your objective only involves w1 but you can still view it as a function of w1,x,y, where the coefficient of w1 is 1, and the coeffs of x,y are zero:

min w1*1 + x*0 + y*0

Once you see this you can formulate it in the usual way as a “standard” LP.