Given investment opportunities of 1, 2 , 3, 4,and 5 , formulate each of the following investment decision scenarios.

a. Choose at most one of the investment opportunities

1+ 2 + 3 + 4 + 5 1

b. Choose at least one of the investment opportunities

1+ 2 + 3 + 4 + 5 1

c. Choose a maximum of three investment opportunities

1+ 2 + 3 + 4 + 5 3

d. Investment 1 cannot be chosen if investment 2 is chosen

1+ 2 1

e. Investment 3 is chosen if and only if investments 4 and 5 are chosen

4 + 5 23

f. Choose either both investments 1 and 5 or choose neither of the two

1= 5

g. Choose at least one of the investments 1, 2, and 3 or at most two investments from 2,3, 4, 5

1+ 2 + 3 1 2 + 3 + 4 + 5 2 + (1 ), y is binary, M is large number.

Could you please explain what M is doing in letter g? It looks like if I1+I2+I3>1 then depending on y the constraint is negative? Please help