Designs Tell specializes in the design and manufacturing of storage cabinets. They have been requested to manufacture a storage cabinet for CDs. For this purpose, the sales department has considered two purchasing options: fully assembled or as a kit. Each cabinet undergoes processing in both the manufacturing and assembly departments. If the manufacturing department produces fully assembled cabinets, it can produce 180 units/day; and if it manufactures kits, it can produce 180 units/day. If the assembly department produces fully assembled cabinets, it can produce 120 units/day; if it produces kits, it can produce 240 units/day. Due to safety regulations, the space for product shipment has a limit of 36,000 units. Each fully assembled cabinet contributes $45 to the company's profits, while each kit contributes $40. a) Write a system of linear inequalities that provide the constraints. b) How many fully assembled cabinets and how many kits should the company produce per day to maximize its profits?