$($CLO $1,$ CLO $3,$ CLO $7)$ Rashed is the production manager for a furmiture manufacturing company. The company produces three products: tables, chairs, and desks. Each table generates a profit of AED$90$ and regritres $7$ hourr of awembly time, $2$ hogr of finisting time, and $8$ units of wood. Each chair gencrates AFD $80$ of profit and requer $6$ bour of ascembly. time, I hour of fimiting thes, and $50$ waits of wood Each desk generates a profit of AED $130$ and requires $2$ hoors of assembly tume, $2$ hours of fininhing time, and $30$ units of wood. There are $480$ hours of asucmbly time, $290$ bours of finishing time, and $1200$ units of wood avalable each month. Rashed was anformed from the marketing department that a manumum quantity of $20$ kables, $15$ chairs should be proinded to a toy al custlomer.

Rasbod uses limear propramming to make best allocation of resources while miceting marker constraints.

Formulate this problem as a linear programming model.

Use Excel QM to solve the Linear programming model and answer the following questions

$21$ What is the product mix?

What is the maximun total profir?

How many hours of finishing tume is used to maximize profic?

Which resources are critical resources? Why?

$25$ What $s$ the impact of one additional unit of wood?

If the profit per desk increases by $20$ AED, what will be the ampact in the total profir?