Q. 155.0( 2 Votes )

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Answer :

Given: Fertilizer ‘A’ consists of 12% nitrogen and 5% phosphoric acid whereas Fertilizer ‘B’ consists of 4% nitrogen and 5% phosphoric acid. ‘A’ costs Rs. 10 per kg and ‘B’ cost Rs. 8 per kg


To find: quantity of fertilizer should be used, so that nutrient requirements are met at a minimum cost


Let the quantity of fertilizer A and B be used as x and y respectively, and the total cost be z


z = 10x + 8y


We need to minimize the cost


Hence, the mathematical formulation of LPP is


Minimize z = 10x + 8y


subject to the constraints,











The feasible region determined by the system of constraints is as follows:



The corner points of the enclosed region are A (0, 300), B(30, 210), C(240, 0)


The value of z at these corners points is as follows:


Case 1: A(0, 300)


z = 10x + 8y


z = 10(0) + 8(300)


z = 0 + 2400


z = 2400


Case 2: B(30, 210)


z = 10x + 8y


z = 10(30) + 8(210)


z = 300 + 1680


z = 1980


Case 3: C(240, 0)


z = 10x + 8y + 370


z = 10(240) + 8(0)


z = 2400 + 0


z = 2400


The value of z is minimum in the second case at point B(30, 210)


Hence, the quantity of fertilizer A and B be used as 30 Kg and 210 Kg respectively, and the total cost is Rs. 1980


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