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Arindam Roy Grade: 11
        

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

6 years ago

Answers : (2)

suryakanth AskiitiansExpert-IITB
105 Points
										

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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Suryakanth –IITB


 

6 years ago
vikas askiitian expert
510 Points
										

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...

6 years ago
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