Maximize values using a grid search?

Questions
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1

enter image description here

I would like to find the maximum value and the optimal m_a and m_d from the above two functions using GRID search. I have tried but it doesn’t work. Do you have any ideas? Any different example of the function with the code would also be great.

f = Integrate[PDF[NormalDistribution[10*Subscript[m, d], 1*Subscript[m, d]], Subscript[c,i]] * (Subscript[m, d]*Subscript[c, i] - 10) * (1-CDF[NormalDistribution[10*Subscript[m, a], 2*Subscript[m, a]], Subscript[c, i]]), {Subscript[c, i], -Infinity, Infinity}]; 
g = Integrate[PDF[NormalDistribution[10*Subscript[m, a], 2*Subscript[m, a]], Subscript[c,i]] * (Subscript[m, a]*Subscript[c, i] - 10) * (1-CDF[NormalDistribution[10*Subscript[m, d], 1*Subscript[m, a]], Subscript[c, i]]), {Subscript[c, i], -Infinity, Infinity}];

NMaximize[f, {Subscript[m, d], Subscript[m, a]},Method -> {"RandomSearch"}];
NMaximize[g, {Subscript[m, d], Subscript[m, a]},Method -> {"RandomSearch"}];

The results show just f and g. It doesn’t work for NMaximize. The screenshot is as follows:

enter image description here

2

how to start a discussion question as I am new to this blog? thank u Sam

3

In[21]:= f[md_?NumericQ, ma_?NumericQ] :=
NIntegrate[
PDF[NormalDistribution[10md, md],
c](mdc - 10)(1 -
CDF[NormalDistribution[10ma, 2ma], c]), {c, -Infinity,
Infinity}]

In[22]:= f[1, 1]

Out[22]= -0.178412

In[23]:= NMaximize[{f[md, ma], md >= 0, ma >= 0}, {md, ma}]

During evaluation of In[23]:= General::stop: Further output of NIntegrate::slwcon will be suppressed during this calculation.

During evaluation of In[23]:= NMaximize::cvdiv: Failed to converge to a solution. The function may be unbounded.

Out[23]= {1.80565*10^18, {md -> 3.23597*10^8, ma -> 5.35716*10^11}}