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.
Let the quantity of fertiliser A and B be x and y resp. To minimize
subject to the constraints :
or
and
and ie
Corner Points Z = 10x+8y
A(0,300)
B(30,210)
C(240,0)
The region of 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.