Use Lagrange multipliers to solve the given optimization problem. Find the maximum value of f(x, y)-xy subject to x + 2y 52.
fmax=
Also find the corresponding point
(x, y)=.

fmax = xy =  26 × 13 = 338

(x,y) = (26,13)

Step-by-step explanation:

Given that:

f(x, y) = xy

subject to x + 2y = 52

So;

x = 52 - 2y

and;

f(x, y) = xy

f(x, y) = (52- 2y) y

f(x, y) =  52y - 2y²

In order to maximize this function;

52y - 2y² = 0

26 y - y² = 0

26 - 2y = 0

-2y = -26

y = -26/-2

y = 13

Again:

x = 52 - 2y

x = 52 - 2(13)

x = 52 - 26

x = 26

fmax = xy =  26 × 13 = 338

(x,y) = (26,13)

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: