1. A manufacturing firm produces two machine parts P1 and P2 of a machine. For this it makes use of milling and grinding machines. The different machining times required for each part, the machining times available on different machines and the profit on each machine part are as given below: Manufacturing Maximum Time Machine Time Required (min) Available P₁ P2 per Week (min) Lathe Milling machine Grinding machine Profit per unit (Rs) 10 1.5 2,500 4 10 2,000 1 1.5 450 50 100 Determine the number of pieces of P1 and P2 to be manufactured per week in order to maximize profit.​