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anonymous
 one year ago
Maximize: Q=4xy^2 where x and y are positive numbers such that x+y^2=6. so.. x=? and y=?
anonymous
 one year ago
Maximize: Q=4xy^2 where x and y are positive numbers such that x+y^2=6. so.. x=? and y=?

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rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0What you could do is differentiate any of the folliwing equations Q = 4(y^2+6)*y^2 or Q = 4x*(x+6)

rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0keep in mind that x and y are greater than 0

rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0@anncaseb which one equation seems easier ?

rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0@anncaseb you're free to ask anything, Im just trying to help you out

rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0in order to find the maximum value we need to simplify one of the equations. lets take this one: Q = 4(y2+6)*y^2 simplifiying: Q = 4y^4+ 24y^2 now you have to differentiate: dQ/dy = 16y^3 + 48y

rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0if we say that dQ/dy = 0 that means the function has a maximum or a minimum value

rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0if we were taking the second equation we should fin out the same answer, lets take a look:

rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0Q = 4x(x +6) Simplifying: Q= 4x^2 +6x Differentiating: dQ/dx = 8x + 6 now when dQ/dx = 0 0 = 8x +6

rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0solve for x and you will find out the maximum value bye

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0or we could do lagrange multipliers ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0Q(x,y) = 4xy^2 Lg(x,y) = L(x+y^26) Qx = 4y^2 Qy = 8xy Lgx = L(1) Lgy = L(2y) 4y^2 = L 2Ly = 8xy ; L = 4x so y^2 = x 2x6 = 0, etc ...

rock_mit182
 one year ago
Best ResponseYou've already chosen the best response.0lagrane multipliers really nice :)
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