A little tricky part 2

Algebra Level 5

Find the product of x x and y y satisfied the maximum value of M M , given that x ∈ [ 0 ; 3 ] ; y ∈ [ 0 ; 4 ] x\in[0;3];y\in[0;4] M = ( 3 − x ) ( 4 − y ) ( 2 x + 3 y ) M=(3-x)(4-y)(2x+3y)


The answer is 0.

P C by P C , 20, Vietnam

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rishabh Jain
Jan 17, 2016

Calculating maximum value of M: \color{#D61F06}{\text{Calculating maximum value of M:}} M = 1 2 ( 6 − 2 x ) 1 3 ( 12 − 3 y ) ( 2 x + 3 y ) M=\frac{1}{2}(6-2x) \frac{1}{3}(12-3y)(2x+3y) = 1 6 ( 6 − 2 x ) ( 12 − 3 y ) ( 2 x + 3 y ) =\frac{1}{6}(6-2x)(12-3y)(2x+3y) Applying AM-GM, M ≤ 1 6 ( ( 6 − 2 x ) + ( 12 − 3 y ) + ( 2 x + 3 y ) 3 ) 3 = 36 M\leq \frac{1}{6}(\frac{(6-2x)+(12-3y)+(2x+3y)}{3})^3=36 For equality: \color{#D61F06}{\text{For equality:}} 6 − 2 x = 12 − 3 y = 2 x + 3 y . . 6-2x=12-3y=2x+3y.. Solving these we get x=0,y=2. x y = 0 \Large xy=0

3 Helpful 0 Interesting 0 Brilliant 0 Confused

y=2, not 6

P C - 5 years, 5 months ago

Log in to reply

Yup.. just a typo.. :)

Rishabh Jain - 5 years, 5 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...