# Question:Problem with rootof and dsolve

## Question:Problem with rootof and dsolve

Maple

Hello,

I have a big problem With maple, it's a bit complicated, but I will try to detail. it's been months since I still looking for the solution :

I have a profit function expressed as follows:

Prof:= L -> int(((P-(50000+50000*exp((.4-theta)/(theta-.1)))/Q(L)-(10+30/theta^.5)*(2000/Q(t))^.4-30*theta*W)*3)*10^9*(W+.1)^.10*(1-(1/25000)*Q(t))*(psi-(1/25000)*Q(t))*exp(-.15*t)/P^2, t = 0 .. L);

Q(t) is the solution of the differential equation:

dQ(t)/t=(3*((10)^(9))*((W+0.1))^(0.1))*(P^(-2))*[1-Q(t)/25000]*[0-Q(t)/25000]

with Q(0)=2000

then :

de:= diff(Q(t),t)=(3*((10)^(9))*((W+0.1))^(0.1))*(P^(-2))*[1-Q(t)/25000]*[0-Q(t)/25000]:
ics:=Q(0)=2000:
dsolve({de,ics},Q(t));

mapel gives me this solution :

After this i need ti inject this solution which correspond to the value of Q(t) in the first equation, and make paratial derivation of Prof(L) respecting to W putting the obtained result equal to zero and solving this equation, to obtain the optimal value of W. The same procedure should be repeated for P and theta (thta varies between 0.1 and 0.4 ) to optain their optimal values which maximise the Profit (Prof function).
I understands all the precedure but I can not do it, I can not find any results. What is it the RootOf ? What is it the value of parametre _a and _Z.

The optimal values optained in the reference for L=2: P=213.9 and W=0.87.

any help is very much appreciate.

Thanks.

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