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GIven that 2x+3y=18, then find the maximum value of x^2y^3.
Dear arindam,
consider (2x/2)2 (3y/3)3
Now sum of the factors of the above expression is
2(2x/2) + 3(3y/3) = 2x+3y
sum of the factors is constant (given 2x+3y = 18) then x2 y3 is maximum when the factors are equal
=> 2x/2 = 3y/3
=> x= y
substuting in the given equation
x = y = 18/5
maximum value is = (18/5)^5
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Askiitians Expert
Suryakanth –IITB
let Z is a function whose maximum value we have to find..
Z= x2 y3
2x +3y =18 (given).............1
Z={ (18-3y)/2 }2 y3 ...........2 (on sustituting x=18-3y/2 from eq 1)
for maxima minima put dZ/dy =0 &
find out different values of y ...put these values in eq 2 and at find the maximum value of this function...
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