Venture capital firm JD is trying to determine in which of 10 projects it should invest. It knows how much money is available for investment in each of the next N years, the NPV of each project, and the cash required by each project in each of the next N years (see the table below).

During year 1, $86 million is available for investment. During year 2, $65 million is available for investment. During year 3, $74 million is available for investment.

Formulate an integer-linear program (ILP) to determine in which projects JD should invest in order to maximize its NPV. (Note: Each project must be completed at either a 100% or 0% level.)

Show how you would modify your model from part a in order to accommodate the following additional requirements.

A) If project 4 is selected, then product 1 must be selected.

B) If Project 4 can be selected only if product 1 is selected.

C) If project 4 is not selected, then product 1 must be selected.

D) If project 4 is not selected, then product 1 must not be selected.

E) Projects 1 and 4 cannot both be selected.

F) At most four projects can be selected.

E) If projects 1, 3, and 5 are all selected, then project 2 must be selected.

F) If projects 1 and 5 are both selected, then neither project 2 nor project 3 can be selected.

E) If either project 1 or 5 is selected, then project 2 must be selected.

F) If project 1 is selected, then either project 2 or project 3 must be selected.

Investment (8 Million) Year 1 Year 2 Year 3 NPV 1 6 3 5 20 2 9 5 7 30 3 12 7 9 40 4 15 9 12 50 Project 5 6 7 18 21 24 11 13 15 12 14 16 60 70 80 8 27 17 11 90 9 30 19 20 100 10 35 21 24 130 Investment (8 Million) Year 1 Year 2 Year 3 NPV 1 6 3 5 20 2 9 5 7 30 3 12 7 9 40 4 15 9 12 50 Project 5 6 7 18 21 24 11 13 15 12 14 16 60 70 80 8 27 17 11 90 9 30 19 20 100 10 35 21 24 130