Question

Arun has to go to the country of Ten to work on a series of tasks for which he must get a permit from the Government of Ten. Once the permit is issued, Arun can enter the country within ten days of the date of issuance of the permit. Once Arun enters Ten, he can stay for a maximum of ten days. Each of the tasks has a priority, and takes a certain number of days to complete. Arun cannot work on more than one task at a time. The following table gives the details of the priority and the number of days required for each task. Arun's first priority is to complete as many tasks as possible, and then try to complete the higher priority tasks. His last priority is to go back as soon as possible. The tasks that Arun should try to complete are:

Task	Priority	Days Required
T1	1	3
T2	2	5
T3	5	3
T4	3	4
T5	4	2

• A. T1 and T2
• B. T1, T2 and T5
• C. T1, T4 and T5
• D. T1, T2 and T4
• E. T1, T3 and T4

Hint:

When multiple objectives are given in order, optimize them lexicographically: first maximize the count, then compare priority scores, and finally use time as a tiebreaker. Feasibility quickly narrows options—here, \(4\) tasks were impossible because the minimum total time exceeded the limit.

Answer 1

The Correct Option is B

To determine which tasks Arun should prioritize to complete as many as possible within the 10-day limit, while considering their priority, we should follow these steps:

Firstly, we list out the tasks along with their corresponding number of days and priorities:

Task	Priority	Days Required
T1	1	3
T2	2	5
T3	5	3
T4	3	4
T5	4	2

Next, the tasks should be selected to maximize task completion, starting with those consuming the fewest number of days, maintaining within the 10-day limit.

Let's attempt a solution using this methodology:

• Select T1 (3 days) + T2 (5 days) + T5 (2 days) = 10 days.
• This includes 3 tasks with the highest priorities: T1, T2, and T5.

Thus, the optimal solution is to complete tasks T1, T2, and T5 within the 10-day stay in the country of Ten.