$4)$ The following is the current iteration $($not initial iteration!$)$ of a given maximization problem. The objective is to maximize $5$x$1+3$x$2,$ and the slack variables are x$3$ and x$4.$ The constraints are of the $<=$ type. Find the unknowns a through g$.($Hint: After finding a$,$b$,$c$,$d and f$,$ trying to insert x$4$ as basic variable in finding e and trying to insert x$2$ as basic variable in finding g$,$ may work!$)(30$ pts$)$

Current Iteration

z X$1$ X$2$ X$3$ X$4$ RHS

$1$ b $1$ f g z$=10$

$0$ c $011/5$ X$3=2$

$0$ d e $01$ X$1=$a