Formulate but do not solve the following exercise as a linear programming problem.

Acoustical Company manufactures a DVD storage cabinet that can be bought fully assembled or as a kit. Each cabinet is processed in the fabrications department and the assembly department. If the fabrication department manufactures only fully assembled cabinets, it can produce $210$ units$/$day; and if it manufactures only kits, it can produce $210$ units$/$day$.$ If the assembly department produces only fully assembled cabinets, it can produce $80$ units$/$day; but if it produces only kits, then it can produce $340$ units$/$day$.$ Each fully assembled cabinet contributes $$60$ to the profits of the company, whereas each kit contributes $$40$ to its profits. How many fully assembled units x and how many kits y should the company produce per day to maximize its profits P in dollars?