Find a feasible solution or determine that no feasible solution exists for the following system of difference constraints: X1 - X3 31 X2 - X3 S-4 X4 - Xs <2 X3 - X4 <7 X5 - x1 55 X4 - x2 3 10 I-5x- 5x

8. A school is creating class schedules for its students. The students submit their requested courses and then a program will be designed to find the optimal schedule for all students. The school has determined that finding the absolute best schedule cannot be solved in a reasonablo time. Instead they have decided to use a simpler algorithm that produces a good but non-optimal schedule in a more reasonable amount of time. Which principle does this decision best demonstrate? O A Unreasonable algorithms may sometimes also be undecidable O B. Heuristics can be used to solve some problems for which no reasonable algorithm exsts O C. efficiency Two algorithms that solve the same problem must also have the same O B. Approximate solutions are often identical to optimal solutions

handwritten solution asap

Obtain the set of necessary and sufficient conditions for the following NLP Minimize Z = 2x - 24x1x2 + 2x% – 3x3 – 24x1x3 – 8x2x3 + 150

Problem: Solve the following equality-constrained optimiza- tion problem using Newton descent algorithm with the initial point (1, 4, 0): min f(x, y, z) = e" + 2y? + 3z2 x,y,z subject to x – 5z = 1 | y + z = 4 Compute the optimal dual variables as well. You have to answered above problem By using Python Programming Language.

Cse