$(30$pts $)$ Consider the following problem. Minimize quad Z$=3$x$\_(1)+2$x$\_(2)$ subject to $\{$:$[2$x$\_(1)+$x$\_(2)>=10],[-3$x$\_(1)+2$x$\_(2)<=6],[$x$\_(1)+$x$\_(2)>=6]$:$\}$ and x$\_(1)>=0,$quadx$\_(2)>=0.($a$)$ Solve this problem graphically. $($b$)$ Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial $($artificial$)$ BF solution. Also identify the initial entering basic variable and the leaving basic variable. $($c$)$ Work through the simplex method step by step to solve the problem.