Geppetto, a young woodcarver, manufactures two types of products: chairs and desks. A chair

sells for $$60$ and uses $$15$ of raw materials. A desk sells for $$80$ and uses $$30$ of raw materials.

Geppetto works $70$ hours a week. The chairs and desks require four types of processing:

preparation, cutting, assembling, and finishing. A chair requires $30$ minutes of preparation, $2$

hours of cutting, $1$ hour of assembling, and $45$ minutes of finishing. A desk requires $45$ minutes

of preparation, $2$ hours of cutting, $90$ minutes of assembling, and $1$ hour of finishing. Assume

Geppetto can obtain all the needed raw materials.

Formulate an LP model to maximize Geppetto's profit for the next week.