Question $2$: $($worth $32$ points$)$ The Classic Furniture Company is trying to determine the optimal quantities to make of six possible products: both tables and chairs made of oak, cherry, and pine. The products are to be made using the following resources: labor hours and three types of wood. Minimum production requirements are as follows: at least $3$ each of oak and cherry tables, at least $10$ each oak and cherry chairs, and at least $5$ pine chairs. The Excel LP solution and sensitivity report are provided below.

Each of the following questions is independent of the others. Avoid YES$/$NO and short answers. The answers should highlighted and then explained to some degree. All needed information is provided below.

You do not need to resolve the problem. If you$\_$conclude that the current information cannot answer a question and the problem must be resolved, just say "The current sensitivity report does not offer adequate information to answer the question and the problem needs to be resolved".

a$)$ What is the profit represented by the objective function and what is the production plan?

b$)$ Which constraints are binding?

c$)$ What is the range over which the unit profit for oak chairs can change without changing the production plan?

d$)$ What is the range over which the amount of available oak could range without changing the combination of binding constraints?

e$)$ The unit profit for pine chairs decreases to $$13?$

f$)$ The company is also required to make at least $20$ pine chairs?

g$)$ The company is required to make no more than $55$ cherry chairs?

h$)$ The number of labor hours expands to $1,320?$

$\backslash$table$[[4,$A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I,$J$