Consider the following LP problem:

$$ Maximize z $=2$x$1+3$x$2$

$$ Subject to:

$$ Constraint $1$: $4$x$1+7$x$2<=115$

$$ Constraint $2$: $3$x$1+2$x$2<=70$

$$ Constraint $3$: x$1$ and x$2>=0$

a$.$ What are the values of x$1$ and x$2$ for the optimal solution?

b$.$ What is the maximum value of z$?$