3.A firm buys castings of P and Q type of parts and sells them as finished products after machining, boring and polishing. The purchasing cost for castings are Rs. 3 and Rs. 4 each for parts P and Q and selling costs are Rs. 8 and Rs. 10 respectively. The per hour capacity of machines used for machining, boring and polishing for two products is given below: Parts Capacity (per hour)QP Machining3050 Boring3045 Polishing4530 The running costs for machining, boring and polishing are Rs. 30, Rs. 22.5 and Rs. 22.5 per hour respectively. Required: Formulate the linear programming problem to find out the product mix to maximize the profit solve the problem with Graphical and simplex methods