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