simple linear programming problem

This is an example from my textbook

Minimize 5x-7y-4z+6t

Subject to 2x+6y+z-t <= 5

5x+3y-6z-2t <= 7

-x-3y+6z+2t <= 6

x,y,z,t > = 0

So this is my code

f = [5 -7 -4 6]
A = [2 6 1 -1
    5 3 -6 -2
    -1 -3 6 2]
B = [5 7 6]
x = linprog(f,A,B)

So do i have to list the linear equality constraint if all variables are greater than zero or is there something wrong with the code?

Answer 1

[Fabio Freschi]

% your code
f = [5 -7 -4 6]
A = [2 6 1 -1
    5 3 -6 -2
    -1 -3 6 2]
B = [5 7 6]

% add lowerbound (0) and upper bound (Inf)
lb = [0 0 0 0]
ub = [Inf Inf Inf Inf]

% solve (Aeq = []; beq = [];)
x = linprog(f,A,B,[],[],lb,ub)

[Steven Lord]

Fabio Freschi is correct. If you look at the description of the lb and ub input arguments on the linprog documentation page you'll see it says "Set Aeq = [] and beq = [] if no equalities exist."

The "Obtain Solution and Lagrange Multipliers" example on that page demonstrates this, solving a problem with bounds (actually, just lower bounds but no upper bounds) but no equality constraints.