$8.$ Solve the following goal programming model graphically and by using the computer: $\backslash [\backslash$begin$\{$array$\}\{$l$\}\backslash$text $\{$ minimize $\}$ P$\_\{1\}$ d$\_\{1\}+$P$\_\{1\}$ d$\_\{1\}^\{+\},$ P$\_\{2\}$ d$\_\{2\},$ P$\_\{3\}$ d$\_\{3\},3$ P$\_\{4\}$ d$\_\{2\}^\{+\}+5$ P$\_\{4\}$ d$\_\{3\}^\{+\}\backslash \backslash \backslash$text $\{$subject to $\}\backslash \backslash \backslash$qquad $\backslash$begin$\{$aligned$\}$ x$\_\{1\}+$x$\_\{2\}+$d$\_\{1\}^\{-\}-$d$\_\{1\}^\{+\}$ & $=800\backslash \backslash 5$ x$\_\{1\}+$d$\_\{2\}^\{-\}-$d$\_\{2\}^\{+\}$ & $=2,500\backslash \backslash 3$ x$\_\{2\}+$d$\_\{3\}-$d$\_\{3\}^\{+\}$ & $=1,400\backslash \backslash$ x$\_\{$j$\},$ d$\_\{$i$\}^\{-\},$ d$\_\{$i$\}^\{+\}$ & $\backslash$geq $0\backslash$end$\{$aligned$\}\backslash$end$\{$array$\}\backslash ]$