CAT 2017 Slot 1 DILR Question & Solution
Data Set
Healthy Bites is a fastfood joint serving three items, burgers, fries and ice cream. It has two employees Anish and Bani who prepare the items ordered by the clients. Preparation time is 10 minutes for a burger and 2 minutes for an order of Ice cream. An employee can prepare only one of these items at a time. The fries are prepared in an automatic fryer which can prepare upto to 3 portions of fries at a time, and takes 5 minutes irrespective of the number of portions. The fryer does not need an employee to constantly attend to it, and we can ignore the time taken by an employee to start and stop the fryer; thus, an employee can be engaged in preparing other items while the frying is on. However fries cannot be prepared in anticipation of future orders.
Healthy Bites wishes to serve the orders as early as possible. The individual items in any order are served as and when ready; however,the order is considered to be completely served only when all the items of that order are served.
The table below gives the orders of three clients and the times at which they placed their orders:
Question 1
Assume that only one client's order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared.
At what time is the order placed by Client 1 completely served?
Solution:
It is given that
1 burger takes 10 minutes
1 ice cream takes 2 minutes and 3 portions of fries take 5 min by the machine (operator is not required).
Client 1 ordered 1 burger, 3 portions of fries and 1 ice cream.
The burger will take 10 minutes to finish. Meantime, rest of the order can be completed.
Question 2
Assume that only one client's order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared.
At what time is the order placed by Client 3 completely served?
Solution:
It is given that
1 burger takes 10 minutes
1 ice cream takes 2 minutes and 3 portions of fries take 5 min by the machine (operator is not required).
Anish or Bani cannot start preparing a new order while a previous order is being prepared.
The first order will be completely done at 10:10.
The second order is two fries and one ice cream, which will be done by 10:15.
The third order is one 1 burger and 1 portion of fries.
The burger will take 10 minutes, by which fries will be ready.
Thus, the third order will be completed by 10:25.
Question 3
Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
At what time is the order placed by Client 2 completely served?
Solution:
It is given that
1 burger takes 10 minutes
1 ice cream takes 2 minutes and 3 portions of fries take 5 min by the machine (operator is not required).
The employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
The first order is 1 burger, 1 ice cream and 3 portions of fries.
Anish can start working on the burger and Bani can start working on the ice cream for the first client at 10:00.
The burger will be done at 10:10, ice - cream at 10:02 and fries at 10:05.
The second order is placed at 10:05. (ice cream and fries)
Bani can work on the ice cream for the second client at 10:05 and also put the fries.
The ice cream will be done by 10:07 but the fries will be done by 10:10.
Thus, order will be completed by 10:10.
Question 4
Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
Also assume that the fourth client came in only at 10:35. Between 10:00 and 10:30, for how many minutes is exactly one of the employees idle?
Solution:
It is given that
1 burger takes 10 minutes
1 ice cream takes 2 minutes and 3 portions of fries take 5 min by the machine (operator is not required).
The employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
The first order is 1 burger, 1 ice cream and 3 portions of fries.
Anish can start working on the burger and Bani can start working on the ice cream.
The burger will be done at 10:10, ice - cream at 10:02 and fries at 10:05.
The second order is placed at 10:05. (ice cream and fries)
Bani can work on the ice cream from 10:05 and also put the fries.
Only Bani will be free from 10:02 to 10:05 - 3 minutes.
The ice cream will be done by 10:07 but the fries will be done by 10:10.
Third order of 1 burger and 1 fries is placed at 10:07.
Bani will immediately start working on the burger. He will finish it by 10:17.
Anish would have finished the first burger at 10:10. Only he is free till 10:17 - 7 minutes.
Thus exactly one person is free for 10 minutes.