HPPPL (HP Prime Programming Language), 5858 57 bytes
The * between 10 and min isn’t necessary, so I removed it.
EXPORT s(m)
BEGIN
return sum([2,3,4,1].*m)+10*min+10min(m);
END;
HPPPL is the programming language for the HP Prime color graphing calculator/CAS.
Example runs:
If it doesn’t have to be a program, then it’s realizable in a 4040 39 bytes one-liner:
m:=[3,5,4,3];sum([2,3,4,1].*m)+10*min+10min(m)