Maximize 3x+y with constraints in Matlab

Question

I need to maximize the equation 3x+y in matlab with the following constraints:

2x+y<=6, x+3y<=9, and x,y>=0

I am having a really hard time figuring out

Answer 1

As @Franck mentioned, you can in general use fmincon to solve optimization problems. However, as your problem is simply a linear programming problem, the solution is much simpler (and guaranteed to be optimal) :

f = -[3 1]; % Note the minus as we want maximization
A = [2 1; 1 3];
b = [6; 9];
LB = [0 0];

[X, FVAL] = linprog(f,A,b,[],[],LB)

Will give:

X =

    3.0000
    0.0000


FVAL =

   -9.0000

Hence the optimum is found at point (3,0) and the resulting value is 9.

Try help linprog to read more about this very usefull function.