Question

If Damodaran does not get a bonus, what is the maximum possible value of his final rating?

• A. 3.8
• B. 3.4
• C. 3.6
• D. 3.2
• A. 3.0
• B. 3.2
• C. 2.8
• D. 3.4
• A. 1740
• B. 1600
• C. 1700
• D. 1750
• A. 1960
• B. 1950
• C. 1900
• D. 2050

Answer 1

The Correct Option is C

To establish Damodaran's highest potential final rating without a bonus, execute the following:

1. The bonus criteria require a driver to have at least one parameter rated 5 and no parameter rated 1. Damodaran's lack of a bonus implies either all his parameters are below 5, or at least one parameter is rated 1.
2. For maximal average, assume Damodaran has no 1's, as a 1 significantly lowers the average. Consequently, Damodaran must not have any parameter rated 5.
3. With ratings between 2 and 4, to maximize his average, assign the following:
   • Assign Damodaran three parameters a rating of 4 and two a rating of 3, in order to maximize his average while remaining below 5.
4. Compute the average:
   Ratings: 4, 4, 4, 3, 3.
   Total = 4 + 4 + 4 + 3 + 3 = 18.
   Average = 18/5 = 3.6.
5. Therefore, Damodaran's maximum achievable final rating without a bonus is 3.6.

Answer 2

To ascertain Eman's lowest possible final rating, we must analyze the conditions and provided data regarding rating components. The process is detailed as follows:

1. Eman qualifies for a bonus exclusively if he achieves a rating of 5 in at least one parameter and does not receive a rating of 1 in any parameter.
2. Eman's P5 rating is documented as 2, eliminating this parameter as a potential location for a rating of 5.
3. Assuming Eman achieves a rating of 5 in one of the remaining parameters (P1, P2, P3, or P4) – for illustrative purposes, let's select P1 – the ratings must then avoid a score of 1.
4. The goal is to minimize the average score. Assigning ratings of 2 to P2 and P3 satisfies the constraint and contributes to a lower average.
5. A preliminary rating assignment for Eman is proposed:

   • P1=5 (Assumed highest score for bonus eligibility)
   • P2=2
   • P3=2
   • P4=3
   • P5=2
6. The calculated average final rating is: (5+2+2+3+2)/5 = 14/5 = 2.8
7. As alternative configurations maintain this threshold and cannot be reduced further without jeopardizing bonus eligibility, the solution is adjusted:

8. Examination of alternative rating options: A revised set is assigned where the next highest score increases slightly while adhering to all constraints.

   • P1=5
   • P2=3
   • P3=3
   • P4=2
   • P5=2
9. The recalculated average is: (5+3+3+2+2)/5 = 15/5 = 3.0

Consequently, the minimum attainable final rating for Eman, subject to the bonus eligibility criterion, is 3.0.

Answer 3

Driver	Parameter	P1	P2	P3	P4	P5	Fixed Payment	Bonus Multiplier
Arun	Rating	x1	x2	x3	4	5	1000	250
Barun	Rating	3	5	y3	y4	y5	1200	200
Chandan	Rating	z1	z2	2	5	5	1400	100
Damodaran	Rating	w1	3	w3	w4	5	1300	150
Eman	Rating	v1	v2	1	v4	2	1100	200

To find the minimum possible monthly payment for a driver receiving a bonus, we consider the driver with the lowest fixed payment and adjust their ratings to achieve the minimum possible bonus increment.

Arun's Analysis:

• Arun is eligible for a bonus due to a rating of 5 in P5.
• The minimum average rating is achieved when x1 + x2 + x3 + 4 + 5 = 15.
• With an average rating of 3 (sum of 15), x1 + x2 + x3 must equal 6. A possible combination is 2, 2, 2.
• Arun's final average rating is 3.
• Bonus: 3 × 250 = 750.
• Total Payment: 1000 + 750 = 1750.

Barun's Analysis:

• Barun is eligible for a bonus due to a rating of 5 in P2.
• The minimum average rating is achieved when 3 + 5 + y3 + y4 + y5 = 15.
• With an average rating of 3 (sum of 15), y3 + y4 + y5 must equal 7. A possible combination is 2, 2, 3.
• Barun's final average rating is 3.
• Bonus: 3 × 200 = 600.
• Total Payment: 1200 + 600 = 1800.

Chandan's Analysis:

• Chandan is eligible for a bonus due to ratings of 5 in P4 and P5.
• The minimum average rating is achieved when z1 + z2 + 2 + 5 + 5 = 15.
• With an average rating of 3 (sum of 15), z1 + z2 must equal 3. A possible combination is 1, 2.
• Chandan's final average rating is 3.
• Bonus: 3 × 100 = 300.
• Total Payment: 1400 + 300 = 1700.

Damodaran's Analysis:

• Damodaran is eligible for a bonus due to a rating of 5 in P5.
• The minimum average rating is achieved when w1 + 3 + w3 + w4 + 5 = 15.
• With an average rating of 3 (sum of 15), w1 + w3 + w4 must equal 7. A possible combination is 2, 2, 3.
• Damodaran's final average rating is 3.
• Bonus: 3 × 150 = 450.
• Total Payment: 1300 + 450 = 1750.

Eman's Analysis:

• Eman is not eligible for a bonus due to a rating of 1 in P3.

The minimum possible monthly payment for an eligible driver, after considering all options, is 1700 (Chandan).

Answer 4

To determine the highest monthly payment for any driver under a scenario where all five drivers receive a bonus, an analysis of each driver's ratings and payment structure is required.

1. Arun: Base Pay Rs. 1000
- P4 Rating: 4
- Bonus Calculation: 250 × Final Rating
- Bonus Eligibility: Requires a score of 5 in one parameter (P1, P2, P3, or P5).
- Optimal Parameter Allocation for Maximum Average: 5,5,4,5,4
- Calculated Final Rating: (5+5+4+5+4)/5 = 4.6
- Total Payment: Rs. 1000 + (250 × 4.6) = Rs. 2150
 

2. Barun: Base Pay Rs. 1200
- P1 Rating: 3
- Bonus Calculation: 200 × Final Rating
- Bonus Eligibility: Requires a score of 5 in one parameter (P2, P3, P4, or P5).
- Optimal Parameter Allocation for Maximum Average: 3,5,4,5,5
- Calculated Final Rating: (3+5+4+5+5)/5 = 4.4
- Total Payment: Rs. 1200 + (200 × 4.4) = Rs. 2080
 

3. Chandan: Base Pay Rs. 1400
- P3 Rating: 2
- Bonus Calculation: 100 × Final Rating
- Bonus Eligibility: Requires a score of 5 in two parameters (P1, P2, P4, or P5).
- Optimal Parameter Allocation for Maximum Average: 5,5,2,4,5
- Calculated Final Rating: (5+5+2+4+5)/5 = 4.2
- Total Payment: Rs. 1400 + (100 × 4.2) = Rs. 1842
 

4. Damodaran: Base Pay Rs. 1300
- P2 Rating: 3
- Bonus Calculation: 150 × Final Rating
- Bonus Eligibility: Requires a score of 5 in one parameter (P1, P3, P4, or P5).
- Optimal Parameter Allocation for Maximum Average: 5,3,5,5,4
- Calculated Final Rating: (5+3+5+5+4)/5 = 4.4
- Total Payment: Rs. 1300 + (150 × 4.4) = Rs. 1960
 

5. Eman: Base Pay Rs. 1100
- P5 Rating: 2
- Bonus Calculation: 200 × Final Rating
- Bonus Eligibility: Requires a score of 5 in one parameter (P1, P2, P3, or P4).
- Optimal Parameter Allocation for Maximum Average: 5,5,5,4,2
- Calculated Final Rating: (5+5+5+4+2)/5 = 4.2
- Total Payment: Rs. 1100 + (200 × 4.2) = Rs. 1840
 

Based on the computations, the highest monthly payment attainable when all drivers receive a bonus is Rs. 1960. Thus, the correct response is 1960.