The article presents one of the possible formulations and solutions of the optimization problem of designing the cross-beams of the combined system, reinforced bongs. The basis for efforts as functions of variable parameters was a displacement method. Approximate analytical depending forces and displacements in beams, and the puffs. Analytical expressions possible to formulate the problem of how to design optimization. The article points out that the problem was posed and solved for a fixed geometry puffs and beams. This narrows the area of optimal solutions, but greatly simplifies the solution itself. The objective function – linear. Restrictions – nonlinear functions, therefore considered the problem relates to the problems of nonlinear programming. Optimum obtained in one of the points of intersection of two active constraints – for tightening strength and maximum permissible deflection of the structure. Because of this discrete mathematical optimum mix does not coincide with the physical, so the solution obtained approximately.