3. Write an optimization problem to find the best location (px, py) to place a tv station broadcast antenna so that the average l1-distance to all the houses in the area is minimized. The location of the N houses are given by (l1,x, l1,y),(l2,x, l2,y),(l3,x, l3,y), . . .(lN,x, lN,y). Note, however, that due to zoning restrictions, the antenna must be located within an industrial area of radius 5 miles, centered at (cx, cy). (a) Write the convex optimization program. Clearly define all cost and constraint equations, decision variables, etc. (b) Implement and solve in CPLEX; explain necessary changes to the formulation required for implementation. Use (cx, cy) = (4, 5) and the locations, li,x, li,y, for three houses are given by {(10, 10),(4, 10),(0, 5)}. Where should the antenna be located?