1. A city will undertake four urban renewal housing projects over the next five
ID: 380074 • Letter: 1
Question
1. A city will undertake four urban renewal housing projects over the next five years. Each project has a different timetable. The following table provides the basic data of the situation:
Year 1
Year 2
Year 3
Year 4
Year 5
Cost (million $) for the project
Annual income (million $) if completed 100%
Project 1
Start
End
5.0
0.05
Project 2
Start
End
8.0
0.07
Project 3
Start
End
15.0
0.15
Project 4
Start
End
1.2
0.02
Budget (million $)
3.0
6.0
7.0
7.0
7.0
Projects 1 and 4 should be finished completely within their durations. The remaining two projects can be finished partially within budget limitations if necessary; however, each project must be at least 30% completed within its duration. At the end of each year, the completed section of a project is immediately occupied by tenants, and a proportional amount of income is realized afterwards.
For example, if 40% of project 1 is completed in year 1 and 60% in year 3 (i.e. nothing is completed in year 2), the associated income over this 5-year planning horizon is calculated as follows:
Year 1 income = 0
Year 2 income = 0.4 × $50,000
Year 3 income = 0.4 × $50,000
Year 4 income = (0.4 + 0.6) × $50,000
Year 5 income = (0.4 + 0.6) × $50,000.
As to the cost of the project, it can be prorated; for example, if 40% of project 1 is scheduled to be completed in year 1, the cost needed in year 1 for the project is 0.4 × $5,000,000. The budget arranged by the city each year for these projects is shown at the bottom of the above table.
Develop a schedule for these four projects, indicating their progress for each year that will maximize the total income over the 5-year horizon.
Year 1
Year 2
Year 3
Year 4
Year 5
Cost (million $) for the project
Annual income (million $) if completed 100%
Project 1
Start
End
5.0
0.05
Project 2
Start
End
8.0
0.07
Project 3
Start
End
15.0
0.15
Project 4
Start
End
1.2
0.02
Budget (million $)
3.0
6.0
7.0
7.0
7.0
Explanation / Answer
Step 1 identify the per million return rate:
Step 2 set priority as per return rate:
The investment schedule is found out,
as per the priority and start and end, with the budget in place:
So the return corresponding to it are:
Year 1 Year 2 Year 3 Year 4 Year 5 Cost (million $) for the project Annual income (million $) if completed 100% Per million return Priority Project 1 Start End 5 0.05 0.01 2 Project 2 Start End 8 0.07 0.00875 4 Project 3 Start End 15 0.15 0.01 3 Project 4 Start End 1.2 0.02 0.016667 1 Budget (million $) 3 6 7 7 7Related Questions
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