Solving symbolic equation approximately

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Mario Wenning
Mario Wenning 2020-3-28
I am trying to solve the equation "P_max_diff" ==0 to find the maxima. I am struggeling because there seems to be not a clear analytical solution. Nevertheless the solution should be something like "0,28468*x_m*v_m". I also tried to use vpasolve without any success. Any help is much appreciated.
%Defining the variables
syms v_m x_m x v
syms p
syms P
%Making assumptions
assume(v_m >= 0)
assume(x_m >= 0)
assume(p >= 0)
assume(x >= 0)
assume(v >= 0)
assume(P >= 0)
assume(P,'real')
%Intergration selling scheme
mu_sell = int(int(P/(v_m*x_m),v,P/x,v_m),x,P/v_m,x_m);
%Differentiating the equation
P_max_diff = diff(mu_sell,P);
%Trying to solve the equation for ==0
P_sell_max = solve(P_max_diff,P,'IgnoreAnalyticConstraints',1)
--> Warning: Unable to find explicit solution. For options, see help.
> In solve (line 317)
In BasicAnalysis (line 31)

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