# 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.

SHAIK AASIF AHAMED
9 years ago
Hello student,
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)18
(8x/100)+(10y/100)12
We shouls maximize Z=3x+y
on solving we get (150,0) and so 150 kg of 1 type fertilizer is to be used