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A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is 25 and that from a shade is 15. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit? Formulate an LPP and solve it graphically.

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Let the number of lamps and shades manufactured be x and y respectively.

Vertices of feasible region are O(0, 0), A(6, 0), B(4,4)and C(0, 10).

P(A) = 150, P(B) = 160, P(C) = 150 and For max. profit no. of lamps = 4 no. of shades = 4 Maximum Profit = ₹ 160

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