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

[Gil]

Yes,
<{infinite solutions with t in [1 0], as you calculated by simplex}
+ {(again an infinity of other solutions with any number) × specific vector d1}
+ {{again an infinity of other solutions with any number} × specific vector d2}>

with values of vectors d1 and d2 as indicated (not found by "normal" Simplex procefure).

Complete solution (composed of 4 terms, of which 2 found by “normal" simplex procedure):

{t ×[x1: 0 :x2: 2 :x3: 2 :x4: 0 :x5: 5 :x6: 0 :x7: 17]

+ (1-t) × [x1: 5 :x2: 2 :x3: [ '11/3' 3.66666666667 ] :x4: 0 :x5: 0 :x6: 0 :x7: [ '121/3' 40.3333333333 ]]

+ mu1× [ 1 1 '1/3' 0 0 1 '26/3' ]

+ mu2 ×[ 0 1 0 0 1 1 4 ]},

with t in [0 1]
and with mu1& mu2 free.