1. Consider the production planning of The Super Fast Manufacturing Company which makes items P and V. The steel requirement for P is 400 gm per piece and that for Vis 3 50 gm per piece. Both P and V, are machined on lathe which takes 85 and 50 minutes respectively, and are processed on a grinder which requires 55 and 30 minutes respectively. Each unit of P consumes 20 minutes of polishing time. The resource availability is:

30 per cent of total machine time is that oflathe, 50 per cent of grinder and the remaining of polishing.
Unit contribution to profits for P and Vis Rs 40 and Rs 30, respectively.
Formulate this as a linear programming model for determining the number of units of P and Vto be produced which would maximise the profits. Given also is the constraint that the company cannot sell more units of item P than of item V.

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Total Machine Time: Total Steel 1,450 hours : 250 kg