in my opinion, this is a simple mathematical programming problem. Although I have almost forgotten, I hope I can help you.

suppose that the number of shares of investment fund a is a million, and that of investment fund b is b million.

the problem can be described as:

5a+1b <; =12 (1)

5a*1%+1b*4%> =6, namely: 5a+4b >; =6 (2)

For 1, simultaneous (1)(2) is available, which is a graphic solution learned in high school. The solution is not unique, and it is a triangular area, so I won't draw the graph.

pair 2, namely 5a+1b <: =12

finding max{5a+4b}

is like a total investment A, that is, a total investment of 1.2 million, with an expected return of 12,.

pair 3, namely 5a+1b <: =12 ,5a+4b> =6

Finding min(8a+3b)

This solution is the only answer. As can be seen from the drawing, simultaneous 5a+1b=12 ,5a+4b=6 is enough.

score: a=.4,b=1, that is, fund A invested 4 shares and fund B invested 1, shares.

for supplementary questions, add 1b >; =3 constraint, the answer remains the same. Or a fund invests 4 copies, and b fund invests 1 thousand copies, with a return of 6 thousand.