CHALLENGE 3: You need to write a SCIP model to solve the following geometric problem: Your problem is packing m of spheres in a box of minimal area. The spheres have a given radius ri, and the problem is to determine the precise location of the centers xi. The constraints in this problem are that the spheres should not overlap, and should be contained in a square of center 0 and half-size R. The objective is to minimize the area of the containing box. Show that two spheres of radius r, r2 and centers 1, 2 respectively do not intersect if and only if - r212 exceeds a certain number, which you will determine Formulate the sphere packing problem as an optimization model. Is the formulation you have found convex optimization? Using your model write SCIP code to solve the packing problem of five and six circular disks of the same radius inside a square of half-size R. What is the optimal size if the disks have radius 1? Do some drawings using MATLAB of the packings you discovered. Is the solution unique? CHALLENGE 3: You need to write a SCIP model to solve the following geometric problem: Your problem is packing m of spheres in a box of minimal area. The spheres have a given radius ri, and the problem is to determine the precise location of the centers xi. The constraints in this problem are that the spheres should not overlap, and should be contained in a square of center 0 and half-size R. The objective is to minimize the area of the containing box. Show that two spheres of radius r, r2 and centers 1, 2 respectively do not intersect if and only if - r212 exceeds a certain number, which you will determine Formulate the sphere packing problem as an optimization model. Is the formulation you have found convex optimization? Using your model write SCIP code to solve the packing problem of five and six circular disks of the same radius inside a square of half-size R. What is the optimal size if the disks have radius 1? Do some drawings using MATLAB of the packings you discovered. Is the solution unique