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 December 6th, 2018, 03:45 AM #1 Newbie   Joined: Dec 2018 From: UK Posts: 2 Thanks: 0 Help with deriving formula Can you help to derive a formula that can calculate b2, b3, b4 where T = a1(b1) + a2(b2) + a3(b3) + a4(b4) a1=a2=a3=a4=0.25 b1+b2+b3+b4=1 b1
 December 6th, 2018, 04:53 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,634 Thanks: 2080 y = T = a1(b1) + a2(b2) + a3(b3) + a4(b4) = 0.25(b1 + b2 + b3 + b4) = 0.25, not 2.
December 6th, 2018, 06:28 AM   #3
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Quote:
 Originally Posted by adam2018 Can you help to derive a formula that can calculate b2, b3, b4 where T = a1(b1) + a2(b2) + a3(b3) + a4(b4) a1=a2=a3=a4=0.25 b1+b2+b3+b4=1 b1
First, your example makes no sense.

Second, your notation is far more complex than it needs to be.

Third, if you are asking for a solution of the following system

$d + p + q + r = 1, \text { and } d < p < q < r.$

Once d is given, you have three unknowns, but only one equation. No unique solution is possible. If, however, you stipulate that

$0 \le d < 0.25 = \dfrac{1}{4}$, you can bound p, q, and r.

EDIT: Perhaps you are trying to work with this system.

$0 < y,\ 0 \le 4x < y, \ p = \dfrac{x}{y},\ p + q + r + s = 1, \text { and } p < q < r < s.$

If x and y are given, p is determined, q, r, and s are bounded, and

$y = py + qy + ry + sy.$

Last edited by JeffM1; December 6th, 2018 at 07:06 AM.

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