Home
Class 12
MATHS
An owner of a lodge plans a extension wh...

An owner of a lodge plans a extension which contains not more than 50 rooms. At least 5 must be executive single rooms. The number of executive double rooms should be at least 3 times the number of executive single rooms. He charges Rs. 1800 for executive single rooms per day and Rs.3000 for executive double room. Formulate the above problem as LPP to maximize the profit.

A

Maximize `z=1800x+3000y` subject to `x+yle50,xge5,yle3x,xge0,yge0`

B

Maximize `z=1800x+3000y` subject to `x+yle50,xle5,yge3x,xge0,yge0`

C

Maximize `z=1800x+3000y` subject to `x+yle50,xge5,yge3x,xge0,yge0`

D

Maximize `z=1800x+3000y` subject to `x+yle50,xle5,yle3x,xge0,yge0`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • LINE

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|127 Videos

  • MATRICES

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|277 Videos

Similar Questions

Explore conceptually related problems

An aeroplane can carry a maximum of 250 passengers. A profit of Rs. 1500 is made on each executive class ticket and a profit of Rs. 900 made on each economy class ticket. the airline reserves at least 30 seats ofr executive class. However at least 4 times as many passengers perfer to travel by economomy class than by excutive class. Formulate LPP in order to maximize the profit for the airline.

An aeroplane can carry a maximum of 200 passengers. A profit of Rs.500 is made on each executive class ticket out of which 20% will go to the welfare fund of the employees. Similarly a profit of Rs.400 is made on each economy ticket out of which 25% will go for the improvement of facilities provided to economy class passengers. In both cases, the remaining profit goes to the airline’s fund. The airline reserves at least 20 seats for executive class. However at least four times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximise the net profit of the airline. Make the above as an LPP and solve graphically. Do you think, more passengers would prefer to travel by such an airline than by others?

Two models of a windowpane are made, two identical glass panes of thickness 3 mm are separated with an air gap of 3mm . This composite system is fixed in the window of a room. The other model consists of a single glass pane of thickness 6mm , the temperature difference being the same as for first model. the ratio of the heat flow for the double pane to that for the single pane is (K_("glass") = 2.5 xx 10^(-4) cal//s.m.^(@)C and K_("air") = 6.2 xx 10^(-6)cal//s.m.^(@)C)

Two models of a windowpane are made. In one model, two identical glass panes of thickness 3 mm are separated with an air gap of 3 mm. This composite system is fixed in the window of a room The other model consist of a single glass pane of thickness 3 mm, the temperature difference being the same as for the first model. the ratio of the heat flow fot the double pane to that for the single pane is ( K_("glass")=2.5 xx10^(-4)cal//s.m.^(@)C and K_("air")=6.2 xx10^(-6)cal//s.m.^(@)C ).

An automobile manufacturer makes automobiles and trucks in a factory that is divided into two shops. Shop A, which performs the basic assembly operation must work 5 man-days on each truck but only 2 man-days on each automobile. Shop B, which performs finishing operations, must work 3 man-days for each automobile or truck that it produces. Because of men and machine limitations, shop A has 180 man-days per week available while shop B has 135 man-days per week. If the manufacturer makes a profit of Rs. 30000 on each truck and Rs. 2000 on each automobile, how many of each should he produce to maximize his profit?, Formulate this as a LPP.

A toy manufacturing farm produces toys T_1 and T_2 each of which must be processed through two machines M_1 and M_2. The maximum availablity of machines M_1 and M_2 per day are 14 hours and 20 hours respectively. Manufacturing of toy T_1, requires 5 hours on machine M_1 If the 3 hours on machine M_2 whereas toy T_2, requires 4 hours on machine M_1, and 6 hours on machine M_2. If the profit on manufacturing of toy T, is Rs.50 and profit on manufacturing of toy T_2 is Rs.70, formulate this problem as L.P.P. in order to maximize the profit.

NIKITA PUBLICATION-LINEAR PROGRAMMING-MCQs
  1. Feasible region is represented by

    Text Solution

    |

  2. The vertex of the linear inequalities 2x+3yle6, x+4yle4,xge0,yge0 is

    Text Solution

    |

  3. The solution set of the constraints x+yle11,3x+2yge25,2x+5yge20,xge0,y...

    Text Solution

    |

  4. The corner points of common region are, if 2x+yge9,x+2yge9,x+yge7andxg...

    Text Solution

    |

  5. A company manufactures two types of chemicals A and B. Each chemical r...

    Text Solution

    |

  6. A furniture manufacturer produces tables and bookshelves made up of wo...

    Text Solution

    |

  7. Diet of a sick person must contains at least 4000 units of vitamins, 5...

    Text Solution

    |

  8. A printing company prints two types of magzines A and B. The company e...

    Text Solution

    |

  9. A dealer wishes to purchase table fans and ceiling fans. He has Rs. 57...

    Text Solution

    |

  10. Shalmali wanto to invest Rs. 50,000 in saving certificates and PPF. Sh...

    Text Solution

    |

  11. If a motorcyclist rides at a speed of 50 km/hr, he has to spend Rs. 2 ...

    Text Solution

    |

  12. Two different kinds of foods A and B are being considered to form a we...

    Text Solution

    |

  13. A shop keeper sells to two items, colour T.V. sets and DVD players. H...

    Text Solution

    |

  14. A factory makes two types of biscuit B(1)andB(2) that cost Rs. 145 and...

    Text Solution

    |

  15. An aeroplane can carry a maximum of 250 passengers. A profit of Rs. 15...

    Text Solution

    |

  16. Two tailors P and Q earn Rs. 350 and Rs. 450 per day respectively. Tai...

    Text Solution

    |

  17. A diet of sick person contains at least 48 units of vitamin A and 64 u...

    Text Solution

    |

  18. The construction company uses concrete blocks made up of cement and sa...

    Text Solution

    |

  19. An owner of a lodge plans a extension which contains not more than 50 ...

    Text Solution

    |

  20. The objective function off LPP defined over the convex set attains it ...

    Text Solution

    |