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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?

Answer»


SOLUTION :Let x kg of type I and y kg of type of type II be used. Then,
`XGE0,yge0,(10)/(100)x+5/100yge14,(6)/(100)x+10/100y ge14.`
COST function is `Z=60/100x+40/100y,i,E,. Z=3/5x+2/5y.`


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