The following tableau represents a specific simplex iteration for a maximization problem. All variables are nonnegative.

$\backslash$table$[[$Basic$,x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,$Solution$],[f,0,-5,0,4,-1,10,0,0,620],[x_8,0,3,0,-2,-3,-1,5,1,12],[x_3,0,1,1,3,1,0,3,0,6],[x_1,1,-1,0,0,6,-4,0,0,0]]$

Use the table to answer the following:

c$)[4$pt$]$ Categorize the variables as basic and non$-$basic and provide the current values of all the variables and the value of the objective function at this iteration.

$($e$.$g$.,$ Basic variables are $...,$ and non$-$basic variables are $...,$

$x_1=$dots,$x_2=$dots,dots,$x_8=$dots,&$f=$dots

d$)2pt$ Is the current solution optimal $($i$.$e$.,$ did Simplex converge$)?$ Why$/$Why not?

e$)4pt$ Identify all non$-$basic variables that have the potential to improve the objective function, and if that variable enters the basic solution, determine the corresponding basic variable to leave the solution.