MATLAB: Linprog unable to solve this problem

linprogMATLAB

I was unable to solve linear program given by
min 2x_1 + 3x_2 + 5x_3 + 2x_4 + 3x_5
subject to x_1 + x_2 + 2x_3 + x_4 + 3x_5 >= 4
           2x_1 - 2x_2 + 3x_3 + x_4 + x_5 >=3
           x_1,x_2,x_3,x_4,x_5 >= 0
Which has the solution of (1,0,0,0,1) which I obtained by solving its dual and using complementary slackness. It can be verified at this website using this command as input:
Minimize 
p=2x1+3x2+5x3+2x4+3x5 
subject to x1+x2+2x3+x4+3x5>=4, 2x1-2x2+3x3+x4+x5>=3, 
           x1>=0, x2>=0, x3>=0, x4>=0, x5>=0 .
But when I tried linprog():
linprog([2 3 5 2 3],[-1 -1 -2 -1 -3; -2 2 -3 -1 -1],[-4;-3])
It says that primal has an unbounded solution. Where am i going wrong with using this command.

Best Answer

How did you specify this constraint in your linprog call?
 x_1,x_2,x_3,x_4,x_5 >= 0
When I add in the lb input to linprog the answer I received agrees with your expected result (to within about 1e-13 or so.)
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