3
$\begingroup$

I hoped someone can help me with 3 simultaneous equations with an additional condition. I can easily solve the following 3 equations using substitution in terms of $S_1$, $S_2$ and $S_3$" $\begin{align*} \text{Eq 1)} &\qquad& (O_{1}-1)S_1 - S_2 - S_3 &= 0.5P\\ \text{Eq 2)} && (O_{2}-1)S_2-S_1-S_3 &= 0.29P\\ \text{Eq 3)} && (O_{3}-1)S_3-S_1-S_2 &=0.21 P \end{align*}$

However, I'm struggling to solve these same equations with an additional condition $\text{Eq4)}\qquad S_1+S_2+S_3 = T.$

Essentially, I want to be able to specify $T$ and calculate the values required for $S_1$, $S_2$ and $S_3$ to make Eq1 50% , Eq2 29% and Eq3 21% of the total.

$O_1$, $O_2$, & $O_3$ are known; $P$ = Eq1+Eq2+Eq3

Any advice is appreciated, thanks. (this is not homework!)

  • 0
    Thanks both Mark & Shai! I've been put back on the right track and used both of your suggestions. Thank you.2011-06-30

2 Answers 2

4

It may be worth noting that $ O_1 S_1 - T = 0.5P $ $ O_2 S_2 - T = 0.29P $ $ O_3 S_3 - T = 0.21P. $

0

Thanks to the help from both Shai Covo and Mark Bennet I've put put back on the right track.

I thought I'd just post up the method I used.

enter image description here