A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?

A factory 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 manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture 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 screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit

A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for at least 5 hours a day. She produces only two items M and N each on the three machines are given in the following table: SHe makes a profit of Rs 600 and Rs 400 on items M and N respectively. How many of each item should she produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum Profit?

A machine takes 5 hours in cutting 120 tools.How many tools will it cut in 20 hours.

Amit took 3/4 hour to paint a table and 1/3 hour to paint a chair .How much time did he take in all?

A furniture firm manufactues chairs and tables, each requairing the use of three machines A,B and C. Producing of 1 chair requires 2 hours of machine A, 1hour on machine B and 1 hour on machine C. Each table requires 1 hour each on machine A and B and 3 hours on machine C. The profit realised by selling 1 chair is Rs 30 while for a table is Rs 60. The total time available per week on machine A is 70 hours , on machine B is 40 hours and on machine C is 90 hours. Find the mathematical formulation so as to find the number of chairs and tables that should be made per week soto maximizethe profit.

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 Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?

A furniture firm manufactures chairs and tables, each requiring the use of three machines A, B and C. Production of one chair requires 2 hours on machine A, 1 hour on machine B and 1 hour on machine C. Each table requires 1 hour each on machine A and B and 3 hours on machine C. The profit obtained by selling on chair is ₹ 30 while by selling one table the profit is ₹ 60. The total time available per week on machine A is 70 hours, on machine B is 40 hours and on machine C is 90 hours. How many chairs and tables should be made per week so as to maximize profit ? Formulate the problem as L.P.P. and sovle it graphically.

A manufacturing company makes two models A and B of a product. Each pice of model a requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of model of B requires 12 labour hours for fabricating and 3 hour for finishing. For fabricating and finishing, the maximum labour hours avaibale are 180 and 30 respectively. the company makes a profit of Rs.8000 on each piece of model A and Rs.12000 on each piece of model B. How many pieces of model A and model B should be manufactured per week to realise a maximum profit? what is the maximum profit per week?