what is the max value of x3y3+3xy,when x+y=8?
A.4144
B.256
C.8192
D.102

• f(x)= x^3*y^3+3xy is a homogeneous function , maxm value of f(x)occurs at x=y
  
  x+y=8 & x=y => x=y=4
  put the value (x,y)=(4,4) in f(x) to get max value of f(x)
  
  f(x)max = 4^3*4^3 + 3*4*4 = 4144
  
• 10 years agoHelpfull: Yes(21) No(3)
• Ans:4144
  
  To know the (x,y) which gives max we have to derivate the given eqn..
  by derivating that we get 3x^2y^2(x+y)+3(x+y)
  by using x+y=8, 24(x^2y^2+1) ----- (1)
  
  the possible combinations for x+y=8 are
  (0,8),(1,7),(2,6),(3,5),(4,4),(5,3),(6,2),(7,1),(8,0)
  we get max value at (4,4) for eqn (1)..
  so now the (x,y)=(4,4)
  
  substituting them original eqn,
  ((4^3)(4^3))+3(4*4)=4144
• 10 years agoHelpfull: Yes(10) No(0)
• the max value wen x+y=8(take x=4 y=4)..
  then [(4^3)*(4^3)*]+(3*4*4)=(4096+48)=4144
  
• 10 years agoHelpfull: Yes(4) No(0)
• x+y=8
  consider possibles of 8(4+4)(6+2)(5+3)(1+7)
  from this apply the values in x3y3+3xy
  so the answer is 4144
  
• 10 years agoHelpfull: Yes(1) No(3)
• given x+y=8, let us take x=4 and y=4
  substitute this in the given equation we get 4144
• 10 years agoHelpfull: Yes(1) No(2)
• A.4144
  the possibilities of x and y vales are(1,7)(2,6)(3,5)(4,4)
  Take X=4 and Y=4 by sub these values in given equ.it gives only the max values
• 10 years agoHelpfull: Yes(1) No(0)
• x+y=8 will gives xy max when x=y so x=y=4
  now x^3*y^3+3xy=(xy)^3+3xy=16^3+16*3=4096+48=4144
• 10 years agoHelpfull: Yes(0) No(0)