A furniture factory is studying the possibility of manufacturing three models of desks: Colonial, Spanish and Canadian. Making each of these desk models will require different amounts of wood, plywood, and particle board. These quantities appear in the following table.

The quantities of wood are in linear meters, the quantities of plywood and particle board are in square meters.

1. The company is considering the possibility of producing 12 colonial style desks, 14 Spanish style desks and 20 Canadian style desks monthly. What quantities of wood should it order monthly to achieve its production objective?

2. The cost of materials is $4.50 per linear meter for wood, $32.50/m for plywood and $22.50/m for particle board. Determine the raw material manufacturing cost matrix.

3. To make a colonial style desk, it takes 6 hours of work. Crafting a Spanish-style desk takes 5 hours and crafting a Canadian-style desk takes 4 hours of work. Knowing that the hourly wage is $8.50, determine the labor cost matrix.

4. Determine the production cost matrix of these offices.

5. The manufacturer wants to make a profit equivalent to 50% of the production costs on these offices. Calculate the manufacturer's price matrix.

6. Furniture is sold in stores that take a 40% profit. Calculate the in-store price matrix.

7. The manager of the lumber company informs the manufacturer that he cannot fulfill his order because he already has contracts with other customers. He then offers to deliver the available quantities each month. The first month's delivery consists of 332 linear meters of wood, 44 square meters of plywood and 44 square meters of particle board. How many desks of each model can be produced with these materials?