Simplex method in prime how to use the constrains maximise s.t. constraints.

[Gil]

Yes, but there are an infinity of solutions
in that special case.

My program on my HP50G EMU48 finds the following general solution:
[ '2/3' 0 '4/3' 0 0 ]
:
+µ[>0]
*
d,
with d : [ 1 1 0 0 0 ].

Try for instance with µ=10
x1: 2/3+10×1
x2: 0+ 10×1
x3: 4/3+10×0
x4: 0+10×0
x5: 0+10×0

And the minimum value remains at 14/3.