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I have 2 equations with 3 variables. I need to find the minimum points for the 3 variables. The question as below:

Equation 1: $$ 0.09518x - 0.06118y - 0.06132z = 4.031 $$ Equation 2: $$ 0.0049x=0.1738 $$ where constraint of $x,y,z$ is $30$ and $50$. Any method to find the minimum points for $x,y$ and $z$? Thanks.

KCL
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  • Do you mean $30\le x,y,z\le 50$ ? – Qwerty Jan 16 '16 at 07:49
  • yes. 30≤x,y,z≤50 – KCL Jan 16 '16 at 07:52
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    The equation 0.0049x=0.5738 is only satisfied if $x = 117.102$, which does not satisfy the constraint $30 \le x \le 50$. So, there are no triples $(x,y,z)$ which satisfy the constraints and the two equations. – JimmyK4542 Jan 16 '16 at 08:31
  • Hi. Thank you for your answer. So sorry I made a serious mistake. For equation 2, should be 0.0049x=0.1738. So x should be 35.47. – KCL Jan 16 '16 at 09:00
  • Is a good habit to add to the question add an 'update' as to what you have been able to proceed upon in the problem after getting help.. More specifically, if you have been able to solve the problem, do mention it as an update. – Qwerty Jan 16 '16 at 09:14

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Hint #1: Each of the two equations defines a plane. The points that satisfy both equations lie on the intersection of these two planes, which is a line. The constraints $30 < x,y,z < 50$ define a 3D box. You're interested in where the line hits the box, I suppose.

Hint #2: Equation #2 is very simple. It gives you immediately that $x = 0.1738/0.0049 =35.47$. So, the line I talked about in hint #1 lies entirely in the plane $x=35.47$. All points of this plane satisfy your constraint $30<x<50$. If you substitute $x=35.47$ into equation #1, you now have a purely 2D problem involving only $y$ and $z$ -- you're asking about the intersection of a line and a rectangle.

bubba
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  • Hi. Thank you for your answer. So sorry I made a serious mistake. For equation 2, should be 0.0049x=0.1738. So x should be 35.47 – KCL Jan 16 '16 at 09:00