State the problem in linear programming terms and solve it using the simplex method.
A furniture manufacturing company plans to make two products chairs and tables from its available resources, which consist of 400 board feet of mahogany timber and 450 man hours of labor. Making a chair requires 5 board feet and 10 man hours and yields a profit of sh. 45/=, while each table uses 20 board feet and 15 man hours and has a profit of sh 80/=. As the production manager you are required to determine how many chairs and tables the company can make keeping within the available resource constraints, so that it maximizes the profit. Let X 1 and X 2 be the production of chairs and tables respectively.