Problem 1 (60 pts). Consider a triangle with vertices (x1,y1), (x2, y2), and (x3, y3). We are inter- ested in inscribing in this triangle k disks so that - the disks touch in no more than one point, - the disks are completely contained in the triangle, and - the disks cover as much of the area of triangle as possible. Note that the disks can have different radii. 1. Formulate this problem as a nonlinear program.