Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




Not registered yet?

  • Index
  •  » Help Me !
  •  » maximize (a-b)(a-c)(a-d)(b-c)(b-d)(c-d) s.t. -1 <= a, b, c, d <= 1

Post a reply

Go back

Write your message and submit
:) :| :( :D :o ;) :/ :P :lol: :mad: :rolleyes: :cool: | :dizzy :eek :kiss :roflol :rolleyes :shame :down :up :touched :sleep :wave :swear :tongue :what :faint :dunno

Go back

Topic review (newest first)

2012-11-14 07:31:34


I am getting the same results through numerical methods, so it looks like your method is fine. Very good!

There is a missing comma in your answer that might cause some confusion.

2012-11-13 22:40:47

I don't know if this method is acceptable but I suppose we could argue like this.

First, we take
so all the factors in the product will be positive. And as we want the product to be as big as possible, we take
to be as big as possible and
to be as small as possible; thus we have

As the expression is now antisymmetrical in
, we can let
is as large as possible); thus we have

Now you can maximize
using normal calculus methods.

2012-11-13 19:57:27

I'll give it one more bump. Please help me out here anyone

2012-11-04 07:24:50

Help from someone?

2012-10-30 08:37:36

I did not have much luck with it either, perhaps they want you to do it by an inequality.

2012-10-30 04:51:48


L(a,b,c,d,u1,u2,u3,u4,u5,u6,u7,u8) = (a-b)(a-c)(a-d)(b-c)(b-d)(c-d) - u1(1-a) - u2(1-b) - u3(1-c) - u4(1-d) - u5(1+a) - u6(1+b) - u7(1+c) - u8(1+d)

and then try to identify which a,b,c,d,u1,u2,u3,u4,u5,u6,u7,u8 that satifies dL/da = dL/db = dL/dc = dL/dd = dL/du1 = ... = 0.

I guess that I've made a misstake when I set up the inequality constraint in L as

dL/du1 = a-1 = 0 => a = 1
dL/du5 = -a-1 = 0 => a = -1

so dL/du1 and dL/du5 cannot be equal to zero at the same time.

2012-10-29 01:52:16

Hi engrymbiff;

How did you set it up?

2012-10-29 01:43:12


Could anybody help me with this problem?

maximize (a-b)(a-c)(a-d)(b-c)(b-d)(c-d) s.t. -1 <= a, b, c, d <= 1

I've tried using Lagrange multipliers but without any luck.

Board footer

Powered by FluxBB