Integer Linear Programming and Advanced Optimization Applications

Integer Linear Programming
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Integer Linear Programming and Advanced Optimization Applications
I have a problem with procrastination. Every day, I tell myself that I will start my work on time, but I always end up putting it off until the last minute. This causes me a lot of stress, and I always feel like I'm behind. A 0,1 integer model for this situation could look like this:
Variables: x1 = start work on time
x2 = procrastinate Objective Function:
Minimize: Z = x1 + x2
Constraints:
x1 + x2 ≥ 1
x1, x2 ≥ 0
There is no optimal solution for this problem, because it is not possible to both start work on time and not procrastinate. However, the integer model can be used to find a solution that is as close to optimal as possible. In this case, the optimal solution would be to start work on time (x1 = 1, x2 = 0). Additionally, linear programming is a powerful tool that can be used to solve optimization problems (Hayes et al., 2022). However, it should be noted that linear programming is only able to optimize linear o...