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# GIven that 2x+3y=18, then find the maximum value of x^2y^3.

105 Points
11 years ago

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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509 Points
11 years ago

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...