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)

answer: a

step-by-step explanation:

10.2 units

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.