A graduating senior has been accepted by three uni- versities for an M.S. in engincering. Two criteria have been identified. The first is the program and university's academic ranking. The second is the cost. A third criteria of location was initially consid- ered, but then the student recognized that it is only for about a year, and applications were only made to acceptable schools. The student is currently enrolled in the first university, which is rated as a 5 for aca- demic rank and a 10 for cost. The second is a larger out-of-state public university, which is rated as an 8 for academic rank and a 6 for cost. The third is a prestigious private school, which is rated as a 10 academically and a 3 for its higher cost. (a) What is the total score for each school if the two objectives have the same weight? (b) If academic rank is has a weight of 75%, what is the total score for each school?

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### Decision-Making for University Selection Based on Academic Rank and Cost

A graduating senior has received acceptance letters from three universities for an M.S. in engineering. The student has identified two crucial criteria for making the final decision:

1. **Academic Ranking:** The program and university's overall academic standing.
2. **Cost:** The financial burden of attending the university.

Initially, the student also considered location, but recognizing its lesser impact for a one-year program, decided to ignore it. All universities considered were deemed satisfactory in terms of location. The following assessments have been made for each university:

- **University 1:** Rated a 5 for academic rank and a 10 for cost.
- **University 2:** A large out-of-state public university rated an 8 for academic rank and a 6 for cost.
- **University 3:** A prestigious private school rated a 10 academically and a 3 due to higher costs.

#### Problem Analysis:
(a) **Objective 1: Equal Weighting**
   - What is the total score for each university if academic rank and cost are considered with equal importance?
   
(b) **Objective 2: Weighted Academic Rank**
   - If academic rank has a weight of 75%, what is the total score for each school?

### Solution Explanation:

#### (a) Equal Weighting Calculation:
To determine the total score with equal weighting (50% for academic rank and 50% for cost), sum the academic rank and cost scores for each university and average them.

- **University 1:**
  \[ \text{Total Score} = \frac{(5 + 10)}{2} = \frac{15}{2} = 7.5 \]

- **University 2:**
  \[ \text{Total Score} = \frac{(8 + 6)}{2} = \frac{14}{2} = 7.0 \]

- **University 3:**
  \[ \text{Total Score} = \frac{(10 + 3)}{2} = \frac{13}{2} = 6.5 \]

#### (b) Weighted Academic Rank Calculation:
Considering academic rank with a 75% weight, and cost with a 25% weight:

- **University 1:**
  \[ \text{Total Score} = (5 \times 0.75) + (10 \times 0.
Transcribed Image Text:### Decision-Making for University Selection Based on Academic Rank and Cost A graduating senior has received acceptance letters from three universities for an M.S. in engineering. The student has identified two crucial criteria for making the final decision: 1. **Academic Ranking:** The program and university's overall academic standing. 2. **Cost:** The financial burden of attending the university. Initially, the student also considered location, but recognizing its lesser impact for a one-year program, decided to ignore it. All universities considered were deemed satisfactory in terms of location. The following assessments have been made for each university: - **University 1:** Rated a 5 for academic rank and a 10 for cost. - **University 2:** A large out-of-state public university rated an 8 for academic rank and a 6 for cost. - **University 3:** A prestigious private school rated a 10 academically and a 3 due to higher costs. #### Problem Analysis: (a) **Objective 1: Equal Weighting** - What is the total score for each university if academic rank and cost are considered with equal importance? (b) **Objective 2: Weighted Academic Rank** - If academic rank has a weight of 75%, what is the total score for each school? ### Solution Explanation: #### (a) Equal Weighting Calculation: To determine the total score with equal weighting (50% for academic rank and 50% for cost), sum the academic rank and cost scores for each university and average them. - **University 1:** \[ \text{Total Score} = \frac{(5 + 10)}{2} = \frac{15}{2} = 7.5 \] - **University 2:** \[ \text{Total Score} = \frac{(8 + 6)}{2} = \frac{14}{2} = 7.0 \] - **University 3:** \[ \text{Total Score} = \frac{(10 + 3)}{2} = \frac{13}{2} = 6.5 \] #### (b) Weighted Academic Rank Calculation: Considering academic rank with a 75% weight, and cost with a 25% weight: - **University 1:** \[ \text{Total Score} = (5 \times 0.75) + (10 \times 0.
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