A furniture manufacturing company planes to make three products – chairs, tables and desks from its available weekly resources, which consist of 400 cubic feet of timber and 500 man-hours of labor. To make a chair, it requires 5 cubic feet of timber and 10 manhours of labor and yields a profit of $25. A table uses 20 cubic feet of timber and 15 man-hours of labor and yields a profit of $40. A desk needs 25 cubic feet of timber and 20 man-hours of labor and yields a profit of $50. Develop a linear optimization model and find optimal product mix.