STILL confused on Solver (tried a different approach) NOT SPAM

please look over my new attempt

the answer for x is suppposed to be 88. I can't seem to get the answer

I am not trying to spam I just tried a new approach. Please Please help.

This is my approach.

clear dlc

%feed composition

z1=.5;

z2=.1;

z3=.15;

z4=.25;

%other given data

F=150;

PD=250;

T=10;

L=150-x;

F=150;

%k-values from chart yi/xi

k1=56;

k2=0.65;

k3=0.175;

k4=0.055;

%total balances

x1=(F*z1)/(k1*x+L);

x2=(F*z2)/(k2*x+L);

x3=(F*z3)/(k3*x+L);

x4=(F*z4)/(k4*x+L);

eqn=k1*x1+k2*x2+k3*x3+k4*x4==1;

sol=solve(eqn);

The only answer I get in command window this time is

>> Project (which is the name of the file)

[Cris LaPierre]

Unrecognized function or variable 'x'.

Try removing the semicolon from the lines you want to see the output from (MATLAB Onramp Ch 2.1)

[Rebecca Reyes]

Do you happen to know how I can fix it to solve for x? I tried so many things...

[Cris LaPierre]

You haven't declared what x is, so your code is returning an error. Did you mean to make it symbolic?

[Rebecca Reyes]

Yes, i think? x is what I'm hoping to solve for in the solver.

Answer 1

[Cris LaPierre]

Assuming x is symbolic

%feed composition
z1=.5;
z2=.1;
z3=.15;
z4=.25;
 
%other given data
F=150;
PD=250;
T=10;
 
syms x  
L=150-x;
 
%k-values from chart yi/xi
k1=56;
k2=0.65;
k3=0.175;
k4=0.055;
 
%total balances
x1=(F*z1)/(k1*x+L);
x2=(F*z2)/(k2*x+L);
x3=(F*z3)/(k3*x+L);
x4=(F*z4)/(k4*x+L);
eqn=k1*x1+k2*x2+k3*x3+k4*x4==1

eqn = 

 sol=solve(eqn)

sol = 

double(sol)

ans = 4×1

150.0000 88.6523 173.8927 395.3987

It looks like there are 4 possible solutions to your equation, of which, a value close to 88 is one of them. If I solve your equation substituting in a value of 88, the result is close to 1.

double(subs(lhs(eqn),x,88))

ans = 1.0052

[Rebecca Reyes]

I see! your explanation really helped!

I just have one last question.

Is there a way to analyze those roots so that I can test them to see which root is closest to one or is the only way to input manually like how you did?

Your example,

double(subs(lhs(eqn),x,88))

double(subs(lhs(eqn),x,173)), etc...

[Cris LaPierre]

If you use the exact values returned, every one of them will give you a result of 1. Otherwise, they wouldn't be a solution to the equation. It sounds like you need to maybe come up with a constraint for the solution, like it must be less than 100, for example.

[Rebecca Reyes]

Oh I see. Thank you!