I would appreciate any suggestions to fix the nnum error associated with NMaximize at the end of this script. Adding ?NumericQ does not help. Maybe I am not using it correctly. Thank you.
In[1]:= f[k_, m_] := 4 k^(2/5) m^(2/5)
In[2]:= h[x1_] := x1^(1/2)
In[3]:= mu[c1_] := (3/2) c1^(-1/2)
In[4]:= e[x1_, k_, m_] := f[k, m] - x1
In[5]:= a[k_, m_] := (k^(3/5) m^(-2/5))/(8/5)
In[6]:= q[x1_, K1_, k_, m_] :=
If[e[x1, k, m] >= 0, a[k, m], a[K1 - k, 1 - m]]
In[11]:= prof[p1_, p1s_, k_, K1_, m_, x1_, g_, gs_, t_,
ts_] := (1 - t) p1 h[x1] -
g k + (ts - t) q[x1, K1, k, m] e[x1, k, m] + (1 - ts) p1s h[
f[k, m] + f[K1 - k, 1 - m] - x1] - gs (K1 - k)
In[12]:= prof[p1, p1s, 0.18217378897121703`, 0.9793049816792121`, \
0.1549715222880414`, 2.3964762912739057`, .4, .601, .6, .399]
Out[12]= -0.383489 + 0.619222 p1 + 0.845456 p1s
In[13]:= MNEBest[p1_, p1s_, g_, gs_, t_, ts_] :=
NMaximize[{prof[p1, p1s, k, K1, m, x1, g, gs, t, ts], k >= 0,
k <= K1, K1 >= 0, m >= 0, m <= 1, x1 >= 0,
x1 <= f[k, m] + f[K1 - k, 1 - m]}, {{k, .1, .2}, {K1, .9,
1}, {m, .1, .2}, {x1, 2.3, 2.4}}]
In[14]:= (*Correct answer for p1 and \
p1s.*)MNEBest[1.207759716810693`, 1.2751220667322407`, .4, .601, .6, \
.399]
Out[14]= {1.44453, {k -> 0.118312, K1 -> 0.96547, m -> 0.131045,
x1 -> 2.37927}}
In[15]:= MNEx1[p1_, p1s_, g_, gs_, t_, ts_] :=
MNEBest[p1, p1s, g, gs, t, ts][[2]][[4]][[2]]
In[16]:= ka[p1_, p1s_, g_, gs_, t_, ts_] :=
MNEBest[p1, p1s, g, gs, t, ts][[2]][[1]][[2]]
In[17]:= K1a[p1_, p1s_, g_, gs_, t_, ts_] :=
MNEBest[p1, p1s, g, gs, t, ts][[2]][[2]][[2]]
In[18]:= ma[p1_, p1s_, g_, gs_, t_, ts_] :=
MNEBest[p1, p1s, g, gs, t, ts][[2]][[3]][[2]]
In[19]:= MNEx1s[p1_, p1s_, g_, gs_, t_, ts_] :=
f[ka[p1, p1s, g, gs, t, ts], ma[p1, p1s, g, gs, t, ts]] +
f[K1a[p1, p1s, g, gs, t, ts] - ka[p1, p1s, g, gs, t, ts],
1 - ma[p1, p1s, g, gs, t, ts]] - MNEx1[p1, p1s, g, gs, t, ts]
In[20]:= Consx1[p1_] := (1.5/p1)^(4)
In[23]:= FindRoot[{MNEx1[p1, p1s, .4, .601, .6, .399] == Consx1[p1],
MNEx1s[p1, p1s, .4, .601, .6, .399] == Consx1[p1s]}, {{p1,
1.2}, {p1s, 1.3}}]
During evaluation of In[23]:= NMaximize::nnum: The function value 0.383489 -0.619222 p1-0.845456 p1s is not a number at {k,K1,m,x1} = {0.182174,0.979305,0.154972,2.39648}.
During evaluation of In[23]:= NMaximize::nnum: The function value 0.383489 -0.619222 p1-0.845456 p1s is not a number at {k,K1,m,x1} = {0.182174,0.979305,0.154972,2.39648}.
During evaluation of In[23]:= NMaximize::nnum: The function value 0.383489 -0.619222 p1-0.845456 p1s is not a number at {k,K1,m,x1} = {0.182174,0.979305,0.154972,2.39648}.
During evaluation of In[23]:= General::stop: Further output of NMaximize::nnum will be suppressed during this calculation.
Out[23]= {p1 -> 1.21803, p1s -> 1.28767}
In[24]:= NSolve[{MNEx1[p1, p1s, .4, .601, .6, .399] == Consx1[p1],
MNEx1s[p1, p1s, .4, .601, .6, .399] == Consx1[p1s] && p1 > 0 &&
p1s > 0}, {p1, p1s}, Reals]
During evaluation of In[24]:= NMaximize::nnum: The function value 0.383489 -0.619222 p1-0.845456 p1s is not a number at {k,K1,m,x1} = {0.182174,0.979305,0.154972,2.39648}.
During evaluation of In[24]:= NMaximize::nnum: The function value 0.383489 -0.619222 p1-0.845456 p1s is not a number at {k,K1,m,x1} = {0.182174,0.979305,0.154972,2.39648}.
During evaluation of In[24]:= NMaximize::nnum: The function value 0.383489 -0.619222 p1-0.845456 p1s is not a number at {k,K1,m,x1} = {0.182174,0.979305,0.154972,2.39648}.
During evaluation of In[24]:= General::stop: Further output of NMaximize::nnum will be suppressed during this calculation.
Out[24]= {{p1 -> 1.21803, p1s -> 1.28767}}
