1. Consider a plate with 15 line segments: The start and end positions for each line segment is given in the table below: Line Segment no, (x1, y1), (x2, y2) 1 85 32 145 159 2 28 241 58 489 3 5 277 170 443 4 86 401 355 344 5 162 250 384 28 6 207 153 328 592 7 243 501 503 570 8 547 258 408 578 9 223 17 483 162 10 421 161 589 18 11 452 372 773 221 12 753 327 531 18 13 696 48 637 218 14 666 540 545 418 15 582 503 781 406 a) Formulate an optimization problem to remove the minimum number of line segments (i.e., to keep the maximum number of line segments) so that the remaining line segments do not cross each other. Make sure to mathematically express the objective function and all constraints. b) Write a code in MATLAB to solve this optimization problem to obtain the optimal solution.