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A famer 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 famer 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
7 years ago
Hello student,
Please find the answer to your question below
Given
A famer has a supply of chemical fertilizer of type I which contains 10% nitrogen and 6% phosphoric acid
14 kg of nitrogen and 14 kg of phosphoric acid is required for a good crop.
type II fertilizer which contains 5% nitrogen and 10% phosphoric acid
The fertilizer type I costs Rs.2.00 per kg and type II costs Rs.3.00 per kg.
Let x kg of nitrogen and y kg of phosphoric acid is used for each fertilizer should be used to meet the requirement and by plotting graphs using LPP we get
Minimum at (100,80) and is equal to Rs.440.

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