Please answer all parts

(a) Consider two disks B1 := y ER2 : yi + yz =1 and B2 : y ER2 : (y1 -1)2 + 13 5 1 of radius 1 in R2. Formulate the problem of finding a centre a E R2 and a radius p E R so that the intersection of the balls B1 0 B2 is contained in the ball B := {y ER2 : lly - all2 5 p} and the radius p is as small as possible as an NLP. (b) For this part, we will generalize our NLP formulation in part (a) to an arbitrary dimensions n and to an arbi- trary number of balls m. Let m and n be a pair of positive integers. Suppose we are given a list of vectors C1, C2, . . ., Cm E Rn and a list of positive real numbers 71, 12, . . ., I'm so that they define m Euclidean balls in Rn: Bi := {y ER" : lly - cill2 Sri} Vie {1, 2, ..., m}. Formulate the problem of finding a centre x E R" and a radius p E R so that the intersection of all the balls m B1, B2, . .., Bm (that is B:) is contained in the ball i=1 B := {y ER" : lly - all2