.) Maximize f(x,y) = x2+y2 subject to the constraint 3x + 7y = 26. b.) First, rewrite the constraint as g(x,y) = 0 by subtracting 26 from both sides: c.) Now, compute all derivatives of f(x,y) - Lg(x,y). d.) Enter the function F(x,y,L). (hint:) which is = f(x,y) - Lg(x,y). e.) Compute all the first partial derivatives of the function you entered above: partial F / partial x = partial F / partial y = partial F / partial L = Now, we set all these partial derivatives equal to zero. Take partial F/partial x which you entered above, set it equal to zero, and solve for L: L= Plug this expression for L into partial F/partial y, set it equal to zero, and solve for x: x = Plug this expression for x into partial F/partial L , set it equal to zero, and solve for y: y = Plug this expression for y into the equation for x you got above to find x: x = You have now found x and y which maximize x2+y2 subject to 3x+7y=26. What is this maximum value of x2+y2? x2+y2 =
a.) Maximize f(x,y) = x2+y2 subject to the constraint 3x + 7y = 26.
b.) First, rewrite the constraint as g(x,y) = 0 by subtracting 26 from both sides:
c.) Now, compute all derivatives of f(x,y) - Lg(x,y).
d.) Enter the function F(x,y,L). (hint:) which is = f(x,y) - Lg(x,y).
e.) Compute all the first partial derivatives of the function you entered above:
partial F / partial x =
partial F / partial y =
partial F / partial L =
Now, we set all these partial derivatives equal to zero.
Take partial F/partial x which you entered above, set it equal to zero, and solve for L:
L=
Plug this expression for L into partial F/partial y, set it equal to zero, and solve for x:
x =
Plug this expression for x into partial F/partial L , set it equal to zero, and solve for y:
y =
Plug this expression for y into the equation for x you got above to find x:
x =
You have now found x and y which maximize x2+y2 subject to 3x+7y=26. What is this maximum value of x2+y2?
x2+y2 =
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