Consider the following LP and its optimal tableau

$($Table $52)$:

max z $5$x$1$ x$22$x$3$

s$.$t$.$ x$1$ x$2$ x$36$

s$.$t$.6$x$1$ x$2$ x$38$

s$.$t$.6$x$1$ x$2$ x$32$

s$.$t$.6$ x$1,$ x$2,$ x$30$

a Find the dual to this LP and its optimal solution.

b Find the range of values of c$1$ for which the current

basis remains optimal.

c Find the range of values of c$2$ for which the current

basis remains optimal.