Home
Class 12
MATHS
A dealer wishes to purchase a number of ...

A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5760 to invest and has space for atmost 20 items. A fan costs him Rs. 360 and a sewing machine Rs. 240. His expectation is that he can sell a fan at pofit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise his profit ?

Text Solution

Verified by Experts

The correct Answer is:
For maximum profit, 8 fans and 12 sewing machines should be purchased.
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER - 12|14 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER - 2 (SECTION - D)|2 Videos
  • MATRICES

    KUMAR PRAKASHAN|Exercise Practice Paper - 3 (Section - D)|1 Videos

Similar Questions

Explore conceptually related problems

A dealer wants to purchase 5 litres oil tin and 1 kg ghee tin. He has only Rs. 5760 to invest and has a space for atmost 20 tins. 5 l oil tin costs him Rs. 360 and 1 kg ghee tin costs him Rs. 240. He can sell oil tin at a profit of Rs. 22 and ghee tin at a profit of Rs. 18. Assuming that he can sell all the items that he buys, how should he invest his money for maximum profit ?

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 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 ?

(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 use of all the three machines. The number of hours required for producing 1 unit of each of M and N 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 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 bag contains some coins of Rs. 5 and some coins of Rs. 2. If the total number of coins is 40 the total amount is Rs. 125, find the number of coins of each denomination.

A wholesale dealer wants to starts the business with Rs. 2,40,000. The cost price of a quintal wheat is Rs. 2000 and the cost price of a quintal rice is Rs. 3000. He has the space capacity for 200 quintals grain. The profit from the sale of one quintal wheat is Rs. 125 and that from one quintal rice is Rs. 200. If he has x quintal rice and y quintal wheat then the objective function for the maximum profit is ............

The cost of 2 pencils and 3 erasers is Rs. 9 and the cost of 4 pencils and 6 erasers is Rs. 18. Find the cost of each pencil and each eraser.

A manufacturer makes two type of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below : Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs. 7.50 and that on each toy of type B is Rs. 5, whow that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

A man starts repaying a loan as first instalment of Rs. 100. If he increases the instalment by Rs 5 every month, what amount he will pay in the 30^("th") instalment?

A man starts repaying a loan as first instalment of Rs 100. If he increases the instalment by Rs 5 every month, what amount he will pay in the 30^(th) instalment?

KUMAR PRAKASHAN-LINEAR PROGRAMMING-PRACTICE WORK
  1. Solve the following linear programming problems graphically : Maximi...

    Text Solution

    |

  2. Solve the following linear programming problems graphically : Minimi...

    Text Solution

    |

  3. A dealer wants to purchase 5 litres oil tin and 1 kg ghee tin. He has ...

    Text Solution

    |

  4. An aeroplane can carry a maximum of 200 passengers. A profit of Rs. 10...

    Text Solution

    |

  5. A housewife wishes to mix together two kinds of food X and Y in such a...

    Text Solution

    |

  6. One kind of cake requires 300 gr of flour and 15 gr of fat and another...

    Text Solution

    |

  7. A factory owner purchase two types of machines A and B for his factory...

    Text Solution

    |

  8. A dealer wishes to purchase a number of fans and sewing machines. He h...

    Text Solution

    |

  9. Two tailors, A and B earn Rs. 15 and Rs. 20 per day respectively. 'A' ...

    Text Solution

    |

  10. A publisher sells a hard cover edition of a text book for Rs. 72 and a...

    Text Solution

    |

  11. Every gram of wheat provides 0.1 gm of proteins and 0.25 gm of carbohy...

    Text Solution

    |

  12. A manufacturer maks two types A and B of tea cups. Three machines are ...

    Text Solution

    |

  13. A medical company has factories at two places, A and B from these plac...

    Text Solution

    |

  14. Kellogg is a new cereal formed of a mixture of bran and rice that cont...

    Text Solution

    |

  15. The brick manufacturer has two depot A and B with stocks of 30,000 and...

    Text Solution

    |

  16. A small firm manufacturers Golden chains and rings. The total number o...

    Text Solution

    |

  17. A company manufactures two articles x and y. There are three departmen...

    Text Solution

    |

  18. A man owns a field of area 1000 sq.m. He wants to plant fruit trees in...

    Text Solution

    |

  19. A factory owner purchase two types of machines, A and B, for his facto...

    Text Solution

    |

  20. A company manufactures the bicycle with gears and without gears in two...

    Text Solution

    |