A furniture company produce and sell chairs, tables and bookshelf. The company has no difficulty in selling its product. However, limited availability of machine time , labor hour and floor space restrict production. Data are given below;

	Chair	Table	Bookshelf	Supply
Machine hr/unit	8	4	5	1000hrs
Labour hr/unit	5	3	3	650hrs
Floor space sq/unit	9	6	9	1260 sq ft
Contribution	270	144	225

Required:

1.Formulate the above problem as a linear programming problem

2.Determine the optimal solution using simplex method

3.The personnel manager of the company claims that by recruiting additional labor force, the combined profit can be increased. Assuming no other charges, is the claim valid ?. Explain the reason

4.Formulate the dual of the above linear programming problem and find the dual solution.