1. (40 points) A company has nine projects under consideration. The NPV added by each project, and the capital required by each project during the next two years, are shown in the following table. (All numbers are in millions.) For example, project 1 will add $14 million in NPV and require expenditures of $12 million during year 1 and $3 million during year 2. $50 million is available for projects during year 1, and $20 million is available during year 2.

• If we can't undertake a fraction of a project, but must undertake either all of a project or none of a project, how can we maximize NPV?
• Suppose that if project 4 is undertaken, then project 6 must also be undertaken. How can we maximize NPV with this requirement? To avoid points to be taken away, please make sure that you set this up so that the constraint can be seen next to data as is shown in the exercise above (see the figures from the previous page).

	millions	millions	millions
	NPV	YEAR 1 EXPENDITURE	YEAR 2 EXPENDITURE
Project 1	14	12	3
Project 2	17	24	7
Project 3	17	6	6
Project 4	15	6	2
Project 5	40	8	5
Project 6	12	6	6
Project 7	14	12	4
Project 8	10	36	3
Project 9	12	18	3