Consider the following linear programming problem:

$$Min$$x$1+2$x$2$

$$s$.$t$.$x$1+3$x$290$

$8$x$1+2$x$2160$

$3$x$1+2$x$2120$

$$ x$270$

$$ x$1,$x$20$

$$

a$.$ Write the problem in standard form. Identify slack$/$surplus variables. $(10$ points$)$

b$.$ The optimal solution of the above LP model is$1807,1507.$ What are the values of the slack and surplus variables at the optimal solution? $(12$ points$)$