question_answer 16)

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 manufacturer a pedestal lamp, while it takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacturer 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 Rs.5 and that from a shade is Rs.3. Assuming that the manufacturer can sell all the lamps and shades that manufacturer can sell all the lamps and shades that he produces, how should be schedule his daily production in order to maximize his profit ? 

Answer:

Let number of pedestal lamps manufactured = x       and number of hours for manufacturing 1 unit of each item is given below :                                 Therefor the above L.P.P. is given as       Maximize, P = 5x + 3y, subject to constraints 2x + y  12, 3x + 2y  20, x , y       L1: 2x + y = 12         L2: 3x + 2y = 20             Here P is maximum at D(4, 4)       Number of Pedestal lamps manufactured = 4       Number of wooden shades manufactured = 4.