$($CLO$.1,$ CLO: $3,$ CLO: $7)$ Rashed is the production manager for a small furniture manufacturing company. The company produces three products: tables, chairs, and desks. Each table generates a profit of AED$90$ and requires $8$ hours of assembly time, $2$ hours of finishing time, and $8$ units of wood. Each chair generates AED $80$ of profit and requires $6$ hour of assembly time, $1$ hour of finishing time, and $50$ units of

wood. Each desk generates a profit of AED $100$ and requires $2$ hours of assembly time, $2$ hours of finishing time, and $30$ units of wood. There are $484$ hours of assembly time, $300$ hours of finishing time,

and $1212$ units of wood available each month

What is the optimal product mix?

What is the maximum total profit?

How many hours of finishing time is used to maximize profit?

Which resource$($s$)$ is $($are$)$ critical?

What is the impact of one additional unit of wood?

What is the impact of one additional unit of finishing time?

If the profit per desk decreases by $15$ AED, will the product mix change: YES or NO$?$

If the profit per Table increases by $30$ AED, the total profit will increase by: