The business school is planning to construct a new Infinity Hub on its Lake Michigan campus to accommodate students enrolled in its MBA program. The school administration has provided the following guidelines for the building design:
1. The Hub must have capacity for at least 1,800 students at any given time.
2. There must be at least one study room for every 50 students.
3. A separate floor must include individual offices for at least 80 faculty members and administrators.
4. Plan A meets the minimum required percentage of open area in the building.
5. The total construction budget must not exceed $200 million.
An architectural firm has submitted three design plans for the new Infinity Hub. Each plan differs in size, layout, and budget. In all plans, the top floor is reserved for faculty and administrative offices.
The table below summarizes the details of each proposed plan.
| Item | Plan A | Plan B | Plan C |
|---|---|---|---|
| Student Capacity | 1800 | 2000 | 2000 |
| Number of Floors | 4 | 5 | 5 |
| Number of Classrooms | 18 | 20 | 25 |
| Number of Study Rooms | 36 | 50 | 38 |
| Number of Faculty Offices | 80 | 85 | 90 |
| Used Area (square feet) | 240,000 | 300,000 | 330,000 |
| Vacant Area (square feet) | 160,000 | 200,000 | 220,000 |
| Total Area (square feet) | 400,000 | 500,000 | 550,000 |
| Total Budget (million USD) | 200 | 215 | 230 |