Home
Class 12
MATHS
There are two types of fertilisers F1 an...

There are two types of fertilisers `F_1` and `F_2` . `F_1` consists of 10% nitrogen and 6% phosphoric acid and `F_2` consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If `F_1` costs Rs 6/kg and `F_2` costs Rs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?

Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    PRADEEP PUBLICATION|Exercise EXERCISE|135 Videos
  • INVERSE TRIGONOMETRIC FUNCTIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|279 Videos
  • MATRICES

    PRADEEP PUBLICATION|Exercise EXERCISE|335 Videos

Similar Questions

Explore conceptually related problems

A farmer has a supply of chemical fertilizer of type A which contains 10 % nitrogen and 6% phosphoric acis and type B fertilizer which contains 5% nitrogen and 10% phosphoric acid. After testing the soil condition of a field, it is found that at least 14 kg of nitrogen and 14 kg of phosphoric acid are required for a good crop. The fertilizer type A costs Rs 5 per kg and type B Rs 3 per kg. How many kilograms of each fertilizer should be used to meet the requirements and the cost be minimum? Using LPP, solve the above problem graphically.

A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?

A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden?

A fruit grower can use two types of fertilizer in his garden, brand P and brand Q. The amounts (in kg) of nitrogen, phosphoric acid, potash, and chlorine in a bag of each brand are given in the table. Tests indicate that the garden needs at least 240 kg of phosphoric acid, at least 270 kg of potash and at most 310 kg of chlorine. If the grower wants to minimise the amount of nitrogen added to the garden, how many bags of each brand should be used? What is the minimum amount of nitrogen added in the garden? If the grower wants to maximize the amount of nitrogen added to the garden, how many bags of each brand should be added? What is the maximum amount of nitrogen added?

Compounds of nitrogen, phosphorus and sulphur such as ammonia, phosphoric acid and sulphuric acid are used in fertilizer industry. Write the chemical equation for the preparation of phosphoric acid (H_3PO_4) from orthophosphorus acid (H_3PO_3)

Wrtie the chemical electronic configuration of nitrogen(N=7) and phosphorous (P=15).

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. That: cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion, 2 kg wheat and 3 kg rice is Rs 70. Find the cost of each item per kg. by using matrix method.

Find the cost of sugar and wheat per kg., if the cost of 7kg. Of sugar and 3 kg, of wheat is Rs. 210. cost of 7kg. wheat and 3 kg, of sugar is Rs. 160. (Use determinants).

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion, 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

PRADEEP PUBLICATION-LINEAR PROGRAMMING-EXERCISE
  1. A merchant plans to sell two types of personal computers – a desktop m...

    Text Solution

    |

  2. A diet is to contain at least 80 units of vitamin A and 100 units of m...

    Text Solution

    |

  3. There are two types of fertilisers F1 and F2 . F1 consists of 10% ni...

    Text Solution

    |

  4. The corner points of the feasible region determined by the following s...

    Text Solution

    |

  5. (Diet problem)A dietician has to develop a special diet using two food...

    Text Solution

    |

  6. A farmer mixes two brands P and Q of cattle feed. Brand P, costing Rs ...

    Text Solution

    |

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

    Text Solution

    |

  8. A manufacture make two types of toys A and B. three machines are neede...

    Text Solution

    |

  9. An aeroplane can carry maximum of 200 passengers, A profit of ₹ 400 is...

    Text Solution

    |

  10. Two godowns A and B have grain capacity of 100 quintals and 50 quintal...

    Text Solution

    |

  11. An oil company has two depots A and B with capacities of 7000 l and 40...

    Text Solution

    |

  12. A fruit grower can use two types of fertilizer in his garden, brand P ...

    Text Solution

    |

  13. A fruit grower can use two types of fertilizer in his garden, brand P ...

    Text Solution

    |

  14. A toy company manufactures two types of dolls, A and B. Market tests a...

    Text Solution

    |

  15. Fill ups In an LPP, the conditions xge0, yge0 are called…………..constrai...

    Text Solution

    |

  16. In a LPP, the linear function which has to be maximised or minimised i...

    Text Solution

    |

  17. The common region determined by all the linear constraints of a LPP is...

    Text Solution

    |

  18. Fill ups If the feasible region for an LPP is unbounded, then the maxi...

    Text Solution

    |

  19. The feasible region for no. LPP is always a .......... polygon.

    Text Solution

    |

  20. Fill ups In an LPP, the optimum value of the objective funciton is alw...

    Text Solution

    |