A maker of wooden furniture can produce three different types of furniture: sideboards, tables and chairs. Two machines are used in the production - a jigsaw and a lathe. The manufacture of a sideboard requires 1 hour on the jigsaw and 2 hours on the lathe; a table requires 4 hours on the jigsaw and none on the lathe; a chair requires 2 hours on the jigsaw and 8 hours on the lathe. The jigsaw can only operate 100 hours per week and the lathe for 40 hours per week. The profit made on a sideboard is £100, £40 on a table and £10 on a chair. Determine how best to use the two machines so as to maximize profits. Your task is to formulate this problem as linear programming problem.