For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. 370. Maximize f ( x , y ) = x y on the ellipse b 2 x 2 + a 2 y 2 = a 2 b 2 .
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. 370. Maximize f ( x , y ) = x y on the ellipse b 2 x 2 + a 2 y 2 = a 2 b 2 .
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints.
370. Maximize
f
(
x
,
y
)
=
x
y
on the ellipse
b
2
x
2
+
a
2
y
2
=
a
2
b
2
.
A cellphone manufacturer has developed a profit model that depends on x number of
cellphones per month sold and y hours per month of advertising, according to the function
P(x, y) = 9x2 + 36xy – 4y? – 18x – 18y,
where P is measured in thousand pesos. If the budgetary constraint is 3x + 4y = 32, use
the method of Lagrange Multipliers to find the maximum profit.