A manufacturing company must choose among a series of new investment projects. The net present value (NPV) of the future stream of returns and capital requirements for each project, along with the available capital funds over the next three years, are summarized as follows. A B $6,300 $10,700 NPV Payoff Year 1 Cap Req. $1,600 $2,300 Year 2 Cap Req. $1,800 $3,700 Year 3 Cap Req. $2,200 $3,400 Candidate Project D C E F $14,000 $6,100 $12,100 $3,000 $4,200 $2,500 $5,900 $1,000 $4,000 $1,200 $2,100 $700 $5,100 $1,600 $3,600 $800 Capital Budget $13,500 $10,600 $15,700 (a) Develop a binary programming model to determine the projects in which to invest, with the goal of maximizing NPV. You do not need to solve the LP. (b) How many total solutions (i.e., both feasible and infeasible) are there in this scenario? (c) Suppose that exactly one of projects E or F (but not both) must be selected. Write the constraint that would represent this business requirement in the LP formulation. (d) (Bonus) Suppose that if project B is selected, then project C must also be selected. (Project C may be selected even if project B is not.) Write the constraint that would represent this business requirement in the LP formulation.

A manufacturing company must choose among a series of new investment projects. The net present value (NPV) of the future stream of returns and capital requirements for each project, along with the available capital funds over the next three years, are summarized as follows. (a) Develop a binary programming model to determine the projects in which to invest, with the goal of maximizing NPV. You do not need to solve the LP. (b) How many total solutions (i.e., both feasible and infeasible) are there in this scenario? (c) Suppose that exactly one of projects E or F (but not both) must be selected. Write the constraint that would represent this business requirement in the LP formulation. (d) (Bonus) Suppose that if project B is selected, then project C must also be selected. (Project C may be selected even if project B is not.) Write the constraint that would represent this business requirement in the LP formulation