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A farmer has a supply of chemical fertilizer of type I which contains 12% nitrogen and 8% phosphoric acid and type II fertilizer which contains 7% nitrogen and 10% phosphoric acid. After testing the soil conditions of a field, it is found that atleast 18 kg of nitrogen and 12 kg of phosphoric acid is required for a good crop. The fertilizer type I costs Rs.3.00 per kg and type II costs Rs.1.00 per kg. How many kilograms of each fertilizer should be used to meet the requirement and the cost be minimum.

A farmer has a supply of chemical fertilizer of type I which contains 12% nitrogen and 8% phosphoric acid and type II fertilizer which contains 7% nitrogen and 10% phosphoric acid. After testing the soil conditions of a field, it is found that atleast 18 kg of nitrogen and 12 kg of phosphoric acid is required for a good crop. The fertilizer type I costs Rs.3.00 per kg and type II costs Rs.1.00 per kg. How many kilograms of each fertilizer should be used to meet the requirement and the cost be minimum.

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
Giventype I which contains 12% nitrogen and 8% phosphoric acid
type II fertilizer which contains 7% nitrogen and 10% phosphoric acid
18 kg of nitrogen and 12 kg of phosphoric acid is required for a good crop.
The fertilizer type I costs Rs.3.00 per kg and type II costs Rs.1.00 per kg
From the above data we can write equations
(12x/100)+(7y/100)\geq18
(8x/100)+(10y/100)\geq12
We shouls maximize Z=3x+y
on solving we get (150,0) and so 150 kg of 1 type fertilizer is to be used

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