A manufacturer produces nuts and bolts. It takes 1 hour of worl in machine A and 3 hours on machine B to produce a package of nuts. It take 3 hours on machien A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 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 bis profit, if he operates his machines for at the most 12 hours a day?

A manufacture produces nuts and bolts for industrial machinery. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts while it takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. If he operates his machines for at most 12 hours then formulate the given data in the form of inequations and show graphically the region representing the solution of these inequations.

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 screw 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 ofRs. 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.

(Manufacturing problem): 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 atleast 5 hours a day. She produces only two items M and N each requiring the sue of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machies are given in the follownig table: She makes a profit of Rs. 600 and Rs. 400 on items M and N respectively. How many of each item should be 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 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 onthe 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?

What is the purpose of adding a food preservative to a packaged food?

Ourselves 3. (a) 3 hrs 26 min × 4 = How many hours and mins?

(Manufacturing problem): A manufacturing company makes two models A and B of a product. Each piece of Model A requires 9 labours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing the maximum labour hors available are 180 and 30 respectively. The company makes a profit of Rs. 8000 on each piece of model Aand Rs. 12000 on each piece of Model B. How many piecesof Model A and Model B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

How Chimpanzees break and open the hard shells for eating the nuts?

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman's time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman's time.In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftman's time. (i) What number of rackets and bats must be made if the factory is to work at full capacity? (ii) If the profit on a racket and on a bat is Rs. 20 and Rs. 10 respectivelh, find the maximum profit of the factory when it works at full capacity.