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

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding cutting machine and a sprayer . It takes 2 h on grinding cutting machine and 3 h on the sprayer to manufacture a pedestal lamp . It takes 1 h on the grinding cutting machine and 2 h on the sprayer to manufacture a shade . On any day, the sprayer is available for at the most 20 h and the grinding cutting machine for at the most 12 h . The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3 . Assuming that the manufacture can sell all the lamps and should he schedule his daily production in order to miximize his profit ?

A factor manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to maufacture a package of screw s A, while it take 6 minutes on automatic and 3 minutes on the hand operated machines to maufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs. 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screw he manufactures, how many packages of each type should the factory owner produced day in order to maximise his profit? Determine the maximum profit.

A manufacturer produces nuts and bolts . It takes 1 hr of work on machine A and 3 hr on machine B to produce a package of nuts and bolts . He earns a profit of Rs 17.50 per package on nuts and Rs 7.00 per package on bolts . How many package of each should be produced each most 12 h a day to maximize the profit?