Example. Farmer Furniture makes chairs, arm-chairs and sofas. the profits are $50 per
chair, $60 per arm-chair and $80 per sofa. The material used to manufacture these items
are fabric and wood. A supplier can provide a maximum of 300 meters of fabric and 350
units of wood each week. Each item requires a certain amount of wood and fabric as well
as a certain assembly time. These are given in the following table
How many chairs, arm-chairs and sofas that the company should make per
week so that the total profit is maximized?
Solution. Let x1, x2 and x3 be respectively the numbers of chairs, armchairs, sofa made
per week. Then,