1.A company considers the following 4 projects:

Project A B C D

capital Investment in year 0 $10000 $6000 $4000 $8000

Net cash flow in year 1 $1600 $1300 -$1500 -$2000

net cash flow in year 2 $4000 $5000 $4000 $5000

net cash flow in year 3 $8000 $1200 $8000 $10200

The MARR is 10% per year. The company has a $20000 budget for the capital investment in year 0.

(a) find NPVs of 4 projects, formulate a binary integer programming problem to select projects that maximizes the total NPV, and determine which projects the company should be select by solving the problem with the Excel solver.

(b)In addition to the budget constraint, we further assume that the total cash flow in year 1 must be nonnegative. Formulate a binary integer programming problem to select projects that maximizes the total NPV, and determine which projects the company should select by solving the problem with the Excel solver.

(c)In addition to the constraint in (b), we further assume that Project C can be chosen only if Project D has been selected and that Projects B and C are mutually exclusive. Formulate a binary integer programming problem to select projects that maximizes the total NPV, and determine which projects the company should select by solving the problem with the Excel solver.