A gardener has supply of fertilizer A which consists of 10% nitrogen and 6% phosphoric acid and fertilizer B which consists of 5% nitrogen and 100/6 phosphoric acid. After testing the soil conditions, he finds that he needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for his crop. If fertilizer A costs 10.60 per kg and fertilizer B costs 8A0 per kg, what is the minimum 'cost at which the farmer can meet the nutrient requirement by using a combination of both types of fertilizers? `R s .1488` b. `R s .1576` c. `R s .1648`

Explanation

Let the quantity of fertilizer A be `x kg`
and B be `y kg`
`"CASE-1"`
`10% of x +5% of y=14`
`=>10/100 xx x +5/100 xx y=14`
`=>0.1x+0.005y=14.....(1)`
`"CASE-2"`
`6/100 xx x +10/100 xx y =14`
`=>0.006x+0.1y=14....(2)`
`(1)-(2) ` we get,
`0.04x-0.05y=0`
`=>4x=5y`
`x=5/4y`
so, eqn `(1)` becomes,
`0.1 xx 5/4 y+0.005y=14`
`=>0.5/4 y+0.05y/1=14`
`=>(0.5y+0.2y)/4=14`
`=>0.7 y=56`
`=>y=80`
`x=5/4y`
`=>x=100 kg`
total cost `=100 xx 10.60 +80 xx 8.40`
`=1732 Rs.`