1. Consider a plate with 15 line segments: The start and end positions for each line segment is given in the table below: (x2, y2) (X1, y) 85 28 5 86 162 207 243 547 223 421 452 753 696 Line Segment 32 241 277 401 250 153 501 258 17 161 372 327 48 540 503 145 58 170 355 384 328 503 408 483 589 773 531 637 545 781 159 489 443 344 28 592 570 578 162 18 221 18 218 418 406 4 6 10 12 13 14 15 582 a) Formulate an optimization problem to remove a subset of line segments so that the remaining line segments have the maximum total length without any crossing among line segments b) Write a code in MATLAB to solve this optimization problem to obtain the optimal solution 1. Consider a plate with 15 line segments: The start and end positions for each line segment is given in the table below: (x2, y2) (X1, y) 85 28 5 86 162 207 243 547 223 421 452 753 696 Line Segment 32 241 277 401 250 153 501 258 17 161 372 327 48 540 503 145 58 170 355 384 328 503 408 483 589 773 531 637 545 781 159 489 443 344 28 592 570 578 162 18 221 18 218 418 406 4 6 10 12 13 14 15 582 a) Formulate an optimization problem to remove a subset of line segments so that the remaining line segments have the maximum total length without any crossing among line segments b) Write a code in MATLAB to solve this optimization problem to obtain the optimal solution