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  • There are two types of fertiliser 'A' and 'B'. 'A' consist of 12% nitrogen and 5% phosphoric acid whereas 'B' consists of 4% nitrogen and 5% phosphoric acid .After testing the soil conditions, farmer finds that he needs

There are two types of fertiliser 'A' and 'B'. 'A' consist of 12% nitrogen and 5% phosphoric acid whereas 'B' consists of 4% nitrogen and 5% phosphoric acid .After testing the soil conditions, farmer finds that he needs at least 12 kg of nitrogen and 12 kg of phosphoric acid  for his crops. If 'A' costs Rs 10 per kg and 'B' cost Rs 8 per kg, then graphically determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost.

 

 

 

 
 
 
 
 

Answers (1)

Let the quantity of fertiliser A and B be x and y resp. To minimize Z= Rs\left ( 10x+8y \right )
subject to the constraints : \frac{12}{100}x+\frac{4}{100}y\geq 12
or 12x+4y\geq 1200
and \frac{5x}{100}+\frac{5y}{100}\geq 12\; or\; 5x+5y\geq 1200
and x\geq 0,y\geq 0  ie 3x+y\geq 300,x+y\geq 240
x\geq 0,y\geq 0
Corner Points                                   Z = 10x+8y
A(0,300)                                          z= 10\times 0+8\times 300= Rs \, 2400
B(30,210)                                        z= 10\times 30+8\times 210= Rs \, 1980
C(240,0)                                          z= 10\times 240+8\times 0= Rs \, 2400
The region of 10x+8y< 1980 has no point in common to the feasible region
so z is minimum for x = 30 and y = 210 and the minimum value of z is Rs 1980. Hence the quantity of fertilizer A is 30 kg and of fertilizer B is 210 kg.

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Ravindra Pindel

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