Home
Class 12
MATHS
A gardener has supply of fertilizer A...

A gardener has supply of fertilizer A which consists of 10% nitrogen and 6% phosphoric acid and fertilizer B which consists of 5% nitrogen and 100/6 phosphoric acid. After testing the soil conditions, he finds that he needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for his crop. If fertilizer A costs 10.60 per kg and fertilizer B costs 8A0 per kg, what is the minimum 'cost at which the farmer can meet the nutrient requirement by using a combination of both types of fertilizers? `R s .1488` b. `R s .1576` c. `R s .1648`

Text Solution

Verified by Experts

Let the quantity of fertilizer A be `x kg`
and B be `y kg`
`"CASE-1"`
`10% of x +5% of y=14`
`=>10/100 xx x +5/100 xx y=14`
`=>0.1x+0.005y=14.....(1)`
`"CASE-2"`
`6/100 xx x +10/100 xx y =14`
`=>0.006x+0.1y=14....(2)`
`(1)-(2) ` we get,
`0.04x-0.05y=0`
`=>4x=5y`
`x=5/4y`
so, eqn `(1)` becomes,
`0.1 xx 5/4 y+0.005y=14`
`=>0.5/4 y+0.05y/1=14`
`=>(0.5y+0.2y)/4=14`
`=>0.7 y=56`
`=>y=80`
`x=5/4y`
`=>x=100 kg`
total cost `=100 xx 10.60 +80 xx 8.40`
`=1732 Rs.`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • JEE MAINS PREVIOUS YEAR

    RD SHARMA|Exercise EXAMPLE|1 Videos

  • MAXIMA AND MINIMA

    RD SHARMA|Exercise Solved Examples And Exercises|306 Videos

Similar Questions

Explore conceptually related problems

A gardener has supply of fertilizer A which consists of 10% nitrogen and 6% phosphoric acid and fertilizer B which consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, he finds that he needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for his crop. If fertilizer A costs 10.60 per kg and fertilizer B costs 8.40 per kg, what is the minimum 'cost at which the farmer can meet the nutrient requirement by using a combination of both types of fertilizers? R s .1488 b. R s .1576 c. R s .1648 d. Rs 1732

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 fanner finds that she needs atleast 14

Knowledge Check

  • Phosphorous acid is

    A
    monobasic acid
    B
    dibasic acid
    C
    tribasic acid
    D
    tetrabasic acid

  • Meta phosphoric acid has the formula

    A
    `H_(3)PO_(4)`
    B
    `HPO_(3)`
    C
    `H_(3)PO_(3)`
    D
    `H_(3)PO_(2)`

  • The formula of meta phosphoric acid is

    A
    `H_(2)PO_(3)`
    B
    `H_(3)PO_(3)`
    C
    `HPO_(3)`
    D
    `H_(4)P_(2)O_(7)`

    • Similar Questions

    Explore conceptually related problems

    A gardener has a supply of fertilizers of the type I which consists of 10% nitrogen and 6% phosphoric acid, and of the type II which consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, he finds that he needs at leat 14 kg of nitrogen and 14 kg of phophoric acid for his crop. If the type-I fetilizer costs 60 paise per kg and the type-II fertilizer costs 40 paise per kg, determine how many kilograms of each type of fertilizer should be used so that the nutrient requirements are met at a minimum cost. What is the minimum cost?

    There are two types of fertilisers ‘A’ and ‘B’. ‘A’ consists of 12% nitrogen and 5% phosphoric acid whereas ‘B’ consists of 4% nitrogen and 5% phosphoric acid. After testing the soil conditions, farmer finds that he needs at least 12 kg of nitrogen and 12 kg of phosphoric acid for his crops. If ‘A’ costs Rs. 10 per kg and ‘B’ cost Rs. 8 per kg, then graphically determine how much of each type of fertiliser should be used so that nutrient requirement are met at a minimum cost.

    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 he soil conditions a farmer finds that she needs at least 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 to that nutrient requirements are met at a minimum cost. What is the minimum cost?

    (Allocation Problem)A farmer has a supply of chemical fertilizer and type I which contains 10% nitrogen and 6% phospheric acid and type II fertilizer which contains 5% nitrogen and 10% phospheric acid. After testing the soil condition of a field, it is found that at least 14 kg of nitrogen and 14kg of phospheric acid are required for a good crop.The fertilizer type I costs ₹.2.00 per kg and the type II ₹ 3.00 per kg.How many kilograms of each fertilizer should be used to meet the requirements and the cost be minimum?

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

    Home
    Profile