Question

Consider the statements:

a. There does not exist a polynomial time algorithm to solve the integer linear programming problem.

b. The main focus of PERT is 'minimizing time'.

Options:
1. Statement a is true; statement b is true.
2. Statement a is true; statement b is false.
3. Statement a is false; statement b is true.
4. Statement a is false; statement b is false.

Answer 1

Statement a, regarding the integer linear programming problem lacking a polynomial time solution, is true. Statement b, which states that PERT focuses on minimizing time, is also true.

Step-by-step explanation:

The student has asked to evaluate two statements:

1. There does not exist a polynomial time algorithm to solve the integer linear programming problem.
2. The main focus of PERT (Program Evaluation Review Technique) is 'minimizing time'.

For statement a, it is currently true that the integer linear programming problem is considered NP-hard, which suggests that no polynomial time algorithm exists for this problem, unless P=NP, which is an unsolved problem in computer science.

Regarding statement b, it is true that the main focus of PERT is on minimizing time. PERT is a project management tool used to schedule, organize, and coordinate tasks within a project, and one of its primary objectives is to reduce the total completion time of the project.