Consider the following linear program P with two resources and three activities. The resources are in the amounts of $12$ and $20,$ where the activities are represented by three variables.

Maximize subject to

and

Z $=20$x$1+15$x$2+5$x$3,6$x$1+4$x$2+2$x$3<=12(1)$

$10$x$1+5$x$2+4$x$3<=20(2)$ x$1>=0,$ x$2>=0,$ x$3>=0.$

Let x$4$ and x$5$ denote the slack variable for functional constraint $(1)$ and $(2),$ respectively. Answer the following independent questions.

$($a$)(16$ pts$.)$ Consider the following simplex tableau associated with some basic solution of Problem P$.$ Using y $(=$CBB$-1)$ and S $(=$B$-1)($which is shown in the appropriate place of the tableau$)$ and Fundamental Insight formulas, fill$-$in the remaining entries of the tableau associated with this basic solution. Show all your work.