1. Trapeze Investments Integer Programming Homework Solution MGMT E-5050
Strategic Resource Allocation and Planning
Trapeze Investments
Integer Programming
Homework Solution

2. Trapeze Investments Trapeze Investments is a venture capital firm that
is currently evaluating six different investment op-
portunities.
There is not sufficient capital to invest in all of these,
but more than one will be selected.
An “0-1” integer programming model is planned to
help determine which of the 6 opportunities to choose.
Variables X1,X2,X3,X4,X5, and X6 represent the six
choices
For each of the following situations, write a constraint
(or several constraints) that would be used.

3. Trapeze Investments 1. At least 3 of these choices are to be selected.
2. Either investment 1 or investment 4 must be
undertaken, but not both.
If investment 4 is selected, then investment 6
must also be selected. However, if investment
4 is not selected, it is still possible to select
number 6.
Investment 5 cannot be selected, unless both
investments 2 and 3 are also selected.
Investment 5 must be selected if both invest-
ments 2 and 3 are also selected.

4. Trapeze Investments REQUIREMENT ‘A’ :
X1 + X2 + X3 + X4 + X5 + X6 => 3
At least 3 of these choices are
to be selected.

5. Trapeze Investments REQUIREMENT ‘B’ : X1 + X4 = 1
Either investment 1 or investment 4
must be undertaken, but not both.

6. Trapeze Investments REQUIREMENT ‘C’ : X4 =< X6
If investment 4 is selected, then investment
6 must also be selected.
However, if investment 4 is not selected, it is
still possible to select number 6.

7. Trapeze Investments REQUIREMENT ‘D’ : 2X5 =< X2 + X3
Investment 5 cannot be selected unless both
investments 2 and 3 are also selected.

8. Trapeze Investments REQUIREMENT ‘E’ : X5 + 1 => X2 + X3
Investment 5 must be selected if both
investments 2 and 3 are also selected.