# is it possible to determine the values ​​of the input parameters ca, cb, cc and cd for which the cc value at the output would be maximal?

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Bosnian Kingdom on 1 May 2019
Commented: Bosnian Kingdom on 4 May 2019
is it possible to determine the values ​​of the initial concentrations ca, cb and cd for which the cc value at the output would be maximal? The differential equations are:
dca/dt=-theta1 * ca-theta2*cA;
dcb/dt= theta1*ca+theta4*cc*theta3*cb-theta5*cd
dcc/dt= theta2*cA+theta3*cb*theta*cC*theta6*cd
dcd/dt= theta5*cb*theta6*cd
Yca=cc/ca0
or is it possible to maximize yield Yca.
Thetas are kinetic parameter and they are known.
ca and cb are concentrations of reactants, while the cc and cd are concentrations of products. cd is also present at the beggining of reaction.

Walter Roberson on 2 May 2019
is cA the same as ca, and is cC the same as cc ?
Is theta distinct from theta1, theta2, theta3, theta4, theta5, theta6, or did you miss a numeric suffix?
Bosnian Kingdom on 3 May 2019
I made mistake. Yes, cA is ca, and cC is cc. And theta is theta4, so the correct equations are:
dca/dt=-theta1 * ca-theta2*cA;
dcb/dt= theta1*ca+theta4*cc*theta3*cb-theta5*cd
dcc/dt= theta2*cA+theta3*cb*theta4*cc*theta6*cd
dcd/dt= theta5*cb*theta6*cd
Walter Roberson on 3 May 2019
Then those are the same equations as your other question that I already described the solutions to.

Alan Weiss on 1 May 2019
Yes, take a look at this example, which has a much more complicated objective function. If your objective function is only the value of Yca at the final point, well, just minimize -Yca(end) as the objective function.
Alan Weiss
MATLAB mathematical toolbox documentation

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Bosnian Kingdom on 4 May 2019
Do I must create another script or?