Solution
Understanding the set :
- There are five cab driver - Arun, Barun, Chandan, Damodaran, and Eman, evaluated on five parameters -
P1: timely arrival
P2: behaviour
P3: comfortable ride
P4: driver's familiarity with the route
P5: value for money
on a scale of 1 to 5.
- final rating of a driver is the average of his ratings in these five parameters
- Two parts of monthly payments - fixed payment and final rating-based bonus
- If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters.
This is a maxima minima set:
In this set not much information is given to us to fill the entire table directly,
Therefore, in this set rather than trying to solve the set directly we will go ahead with the questions and solve the set according to them.
| Name | P1 | P2 | P3 | P4 | P5 | Final Rating | Fixed Payment | Bonus Formula |
|---|---|---|---|---|---|---|---|---|
| Arun | 4 | Rs.1000 | Rs.250 × Final Rating | |||||
| Barun | 3 | Rs.1200 | Rs.200 × Final Rating | |||||
| Chandan | 2 | Rs.1400 | Rs.100 × Final Rating | |||||
| Damodaran | 3 | Rs.1300 | Rs.150 × Final Rating | |||||
| Eman | 2 | Rs.1100 | Rs.200 × Final Rating |
Question says,
If Damodaran does not get a bonus, what is the maximum possible value of his final rating
Firstly, Damodaran does not get a bonus
Now, there are two conditions on which a person does not get a bonus,
-
if he/she scores 1 in any of the parameter.
-
If he/she does not get 5 in any of the parameter.
Now, since we need to maximize the score, we will give him 5 in maximum parameters and one "1" which will make him ineligible for bonus-
Thus, the maximum value of the range of ratings that he can acquire would be 1+3(given)+5+5+5.
However, based on condition 2, he can have similar ratings in only two of the parameters.
Thus, the maximum value of the final rating would be (1+3+5+5+4) /5 = 18/5 = 3.6