Blending problems are global optimization problems where the cheapest product has to be determined. A product is as mixture of raw materials having quadratic constraints in its design. These problems are characterized by an initial search space determined by a regular n+1 dimensional simplex (n-simplex). Branch and bound algorithms have been used to perform an exhaustive search of the solution. This search divides the problem into smaller sub-problems by partitioning the search space until a given precision on the solution is reached. The search avoids visiting some sub-problems when it is known they do not contain the best solution. In this work we study the longest edge (LE) partition method for the unit simplex. This division method avoids the generation of needle or non-rounded shapes of sub-simplices, guaranteeing the convergence. We are interested in determining the number of generated simplices in the worst case, i.e., no subspace is rejected. This number is unique for n<3 because the generated sub-simplices are regular or they have just one LE, but this is not the case for n>2. We are interested in knowing the best LE partition in terms of the number of generated sub-simplies, their roundeness and the number of their different shapes. Results of our preliminary studies will be shown in ICCOPT 2013.