simple linear programming problem

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Ricardo Machado
Ricardo Machado 2019-9-20
评论： Steven Lord 2019-9-20
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?

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采纳的回答

Fabio Freschi
Fabio Freschi 2019-9-20
% 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)
  1 个评论
Steven Lord
Steven Lord 2019-9-20
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.

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