You have been retained by the City Council to assist them in allocating remaining funds in this year’s budget. There are nine projects they can choose from:

1. Hire seven new police officers
2. Upgrade police HQ building
3. Buy two new police cruisers
4. Give bonuses to neighborhood resource police officers
5. Buy one new fire truck
6. Hire an assistant fire chief
7. Restore cuts to school sports programs
8. Restore cuts to school music programs
9. Buy new computers for the school district

The City Council surveyed 500 residents and asked them to rate these projects from 0 (low priority) to 9 (high priority) and they totaled the responses to get a “preference score” for each project. The Council stated that it is not bound by this score, but that it would be used as part of their decision making process. Information on the nine projects is summarized in the table below:

Project #	Name	Cost	New Jobs Created	Preference Score
1	Hire seven new police officers	$400,000	7	4176
2	Upgrade police HQ building	$350,000	0	1774
3	Buy two new police cruisers	$50,000	1	2513
4	Give bonuses to neighborhood resource police officers	$100,000	0	1928
5	Buy one new fire truck	$500,000	2	3607
6	Hire an assistant fire chief	$90,000	1	962
7	Restore cuts to school sports programs	$220,000	8	2829
8	Restore cuts to school music programs	$150,000	3	1708
9	Buy new computers for the school district	$140,000	2	3003

The following constraints limit their choices:

• There is $900,000 remaining in the budget
• The Council feel they must create at least 10 new jobs
• Police-related projects are popular, but they must be fair to other sectors (i.e. fire and education) so at most three police-related projects can be funded
• Due to spare-parts storage issues, the City can handle either the new fire truck, or the new police cruisers, but not both
• In order to be fair to both the sports and the arts, the Council feels that it cannot restore cuts to one and not the other. Thus either the cuts to both are restored, or neither cuts are restored
• As part of the agreement with the Teacher’s Union that led to education cuts last year, any new funding this year must go to restoring cuts before new projects are undertaken. Thus the computers cannot be purchased unless the cuts to sports and music are also restored

  You are tasked to develop a decision model that will maximize public support (i.e. preference score) for the selected projects subject to these constraints

  1. What are your decision variables?
  2. What is your objective function?
  3. What are your constraints?
  4. What is the optimal set of projects to fund?