Location problems in regions with and block norms

We consider the two well knownminimax and minisum single facility location problems in the plane which has been divided into two regions, and by a straight line. The two regions are measured by various norms. We focus on three special cases in which the regions and are measured by and norms, and block norms, two distinct block norms. Based on the properties of block norms then we use linear or almost linear problems in different cases to achieve the optimal solution.