Formulate but do not solve the following exercise as a linear programming problem.
Acoustical Company manufactures a CD storage cabinet that can be bought fully assembled or as a kit. Each cabinet is processed in the fabrication 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 110 units/day; but if it produces only kits, then it can produce 310 units/day. Each fully assembled cabinet contributes $60 to the profits of the company, whereas each kit contributes $30 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?
Maximize P, subject to the constraints:
Fabrication department: x ≥ 0
Assembly department: y ≥ 0
Formulate but do not solve the following exercise as a linear programming problem.
A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. In a certain week, the company has 3600 board feet of wood available and 480 labor-hours. If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars?
Maximize P, subject to the constraints:
Board feet: x ≥ 0
Labor-hours: y ≥ 0