$[6\mathrm{.}52]$ Consider the following optimal tableau of a maximization problem

where the constraints are of the $$ type:

a$.$ Find the optimal objective value $.$

b$.$ Would the solution be altered if a new activity $x_9$ with coefficients

$(6,0,-3{)}^t$ in the constraints, and price of $7,$ were added to the

problem?

c$.$ How large can $b_1($the first constraint resource$)$ be made without

violating feasibility?