$.($a$)$ What are the ranges of optimality for the profit of Product $1,$ Product $2,$ Product $3,$ and Product $4?$

$($b$)$ Find the shadow prices of the three constraints and interpret their meanings. What are the ranges in which each of these shadow prices is valid?

$($c$)$ If the profit contribution of Product $4$ changes from $$10$ per unit to $$20$ per unit, what will be the optimal solution? What will be the new total profit? $($Note: Answer this question by using the sensitivity results given above. Do not solve the problem again$).$

$($d$)$ Which resource should be obtained in larger quantity to increase the profit most? $($Note: Answer this question using the sensitivity results given above. Do not solve the problem again$).$