Binary integer programming model (capital budgeting)

PLEASE PROVIDE DETAILED DESCRIPTION AND CACULATIONS IN EXCEL

Problem 2

ML Inc. is considering a set of 10 capital investment projects which
require cash outflows over each of the next three years. The firm wants
to select the optimal portfolio of these projects given the three budget
constraints.

CASH OUTFLOWS

PROJECT YEAR 1 YEAR 2 YEAR 3 NPV

X1 $250 $200 $100 $60

X2 300 250 150 80

X3 275 250 175 55

X4 225 225 50 50

X5 150 250 150 25

X6 400 150 0 100

X7 200 150 100 90

X8 350 50 25 40

X9 250 100 150 75

X10 175 175 175 75



Budget constraints: K1 <= $2,000; K2 <= $1,500; K3 <= $1,000.

Consider that the firm can carry forward unused budget dollars from one
year to the next and that these funds can be invested in a CD to earn a
5% return from one year to the next.

Consider that we are formulating a binary integer programming model for
the capital budgeting problem:

The following interrelationships exist between the projects:

Only X6 or X7 can be accepted; not both.

If X6 is accepted, X2 cannot be accepted.

If X7 is accepted, X8 must be accepted.

X9 and X10 are mutually exclusive, but one must be accepted.

If projects 2 and 4 are accepted in combination, 120% of the NPV will be
generated and the cost will only be 85% of the combined cash outflows
for the two projects separately.

Define the decision variables for this formulation.

Show the binary integer programming formulation including the objective
function and all relevant constraints.

Solve the problem as a binary integer programming model on a
spreadsheet, or in LINDO.

Interpret this solution to management in its language.