Another approach from start -

We could fit polynomials to the data

Input := 


fa[t_] = Fit[adata,{1,t,t^2,t^3,t^4,t^5},t]

Output =


                                     2

0.983247 - 0.0538534 t + 0.00115793 t  - 

                3             -8  4             -10  5

  0.0000118174 t  + 5.66228 10   t  - 1.01836 10    t

Input := 


faPlot = Plot[fa[t],{t,0,200},PlotRange->{{0,200},{0,1}}]

Output =


-Graphics-

Input := 


Show[faPlot,adataPlot]

Output =


-Graphics-

Input := 


fb[t_] = Fit[bdata,{1,t,t^2,t^3,t^4},t]

Output =


                                        2

0.491081 + 0.00114856 t - 0.0000633133 t  + 

            -7  3             -10  4

  2.55029 10   t  - 1.27333 10    t

Input := 


fbPlot = Plot[fb[t],{t,0,200},PlotRange->{{0,200},{0,1}}]

Output =


-Graphics-

Input := 


Show[fbPlot,bdataPlot]

Output =


-Graphics-

Input := 


fc[t_] = Fit[cdata,{1,t,t^2,t^3,t^4},t]

Output =


                                         2

-0.0195834 + 0.0087579 t + 0.0000622727 t  - 

            -7  3             -9  4

  8.81846 10   t  + 2.38368 10   t

Input := 


fcPlot = Plot[fc[t],{t,0,200},PlotRange->{{0,200},{0,1}}]

Output =


-Graphics-

Input := 


Show[fcPlot,cdataPlot]

Output =


-Graphics-

We compute a net return function based on our polynomial fitted curves.

Input := 


nPcost[t_] = - .005 t -.5 fa[t] + 3.5 fb[t] +  .25 fc[t];  

Input := 


Plot[nPcost[t],{t,0,200}]

Output =


-Graphics-

We recall the fitted model to our differential equation solution, Pcost(t).

Plot[Pcost[t],{t,0,200}]

We now compute the optimal net return using our polynomial fitted functions and see that we do not do as well.

We note that we did better, i.e., our net return was higher with the differential equation model.