$7-29$ Graphically analyze the following problem: $\backslash [\backslash$begin$\{$array$\}\{$lrl$\}\backslash$text $\{$ Maximize profit $\}=$ & $\backslash$$ $4$ X$+\backslash$$ $6$ Y & $\backslash \backslash \backslash$text $\{$ subject to $\}$ & X$+2$ Y & $\backslash$leq $8\backslash$text $\{$ hours $\}\backslash \backslash$ & $6$ X$+4$ Y & $\backslash$leq $24\backslash$text $\{$ hours $\}\backslash$end$\{$array$\}\backslash ]$ a$.$ What is the optimal solution? b$.$ If the first constraint is altered to

X$+3$Y$<=8$

$,$ does the feasible region or optimal solution change?