Solve the following goal programming model graphically: Minimize

P

$1$

$$

d

$1$

$$

$$

$,$P

$2$

$$

d

$2$

$$

$$

$,$P

$3$

$$

d

$3$

$$

$$

$,$P

$4$

$$

d

$2$

$+$

$$

$,$P

$5$

$$

d

$3$

$+$

$$

Subject to:

$2$x

$1$

$$

$+6$x

$2$

$$

$+$d

$1$

$$

$$

$$d

$1$

$+$

$$

$=2100$

$\backslash [\backslash$begin$\{$array$\}\{$l$\}5$ x$\_\{1\}+4$ x$\_\{2\}+$d$\_\{2\}^\{-\}-$d$\_\{2\}^\{+\}=3000\backslash \backslash 2$ x$\_\{1\}+2$ x$\_\{2\}+$d$\_\{3\}^\{-\}-$d$\_\{3\}^\{+\}=1400\backslash \backslash$ x$\_\{1\},$ x$\_\{2\},$ d$\_\{$i$\}^\{-\}$ d$\_\{$i$\}^\{+\}\backslash$geq $0\backslash$text $\{$ for $\}$ i$=1,2,3\backslash$end$\{$array$\}\backslash ]$ Indicate the optimal solution and state achievement or non$-$achievement of each goals.

Solve it and provide it clearly