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A farmer has a supply of chemical fertilizer of type I which contains 10% nitrogen and 6% phosphoric acid and type II fertilizer which contains 5% nitrogen and 10% phosphoric acid. After testing the soil conditions of a field, it is found that atleast 14 kg of nitrogen and 14 kg of phosphoric acid is required for a good crop. The fertilizer type I costs Rs.2.00 per kg and type II costs Rs.3.00 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 10% nitrogen and 6% phosphoric acid and type II fertilizer which contains 5% nitrogen and 10% phosphoric acid. After testing the soil conditions of a field, it is found that atleast 14 kg of nitrogen and 14 kg of phosphoric acid is required for a good crop. The fertilizer type I costs Rs.2.00 per kg and type II costs Rs.3.00 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
6 years ago
HELLO STUDENT,
given 14 kgs of nitrogen and phosporus are needed and cost must be minimum.
After plotting Graphically and solving the equations
We get that minimum cost is Rs.440
and 100 kgs of fertilizer A and 80 Kgs of fertilizer B should be used
Thanks and Regards
Shaik Aasif
askIITians faculty

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