a company would like to make the analysis of two commodities which can be produce from the idle time of labour and machine. the co. found on inspection that the labour requirement for the first and the second commodities was 2 and 3 hours respectively and the total available man houre was 24. only product 1 requires machine hour utilization of one hour per unit and at present only 9 spare machine hours are available. product 2 requires one unit of a by-product per unit and the daily availability of the by-product is 6 units. according to the marketing department the sales potential of product 1 cannot exceed 5 units. in a competitive market, product 1 can sold at a profit of Rs. 3 and product 2 at a profit of Rs. 5 per unit. formulate the problem as a linear programming problem and solve the problem with graphical solution and simplex methods interpret the result