Problem $1.(12$ points$)$ XYZ Health is a new start$-$up company producing medical gloves and masks. Each medical glove requires $6$ minutes of labor and $20$ grams of plastic material. Each medical mask requires $12$ minutes of labor and $15$ grams of plastic material. XYZ Health will sell the medical glove and mask with price $8$ HKD and $12$ HKD per unit respectively. XYZ Health has $6$ hours of labor and $700$ grams of plastic material.

$($a$)$ Formulate the linear programming problem to maximize the profit of XYZ Health. Use the graphical method by hand to solve the problem.

$($b$)$ Let $\backslash (\backslash$mathbf$\{$b$\}\backslash )$ be the amount of plastic material XYZ Health has. What is the sensitive range and shadow price of $\backslash (\backslash$mathbf$\{$b$\}\backslash )?$