Optimal design of a rotary cutter by Lagrangian Multipliers for the continuous production of Indian unleavened flat bread

A mathematical approach based on the use of Lagrangian Multipliers for optimal design of a rotary cutter for continuous production of chapatis (Indian unleavened flat bread), is presented. The objective was max. chapati yield; constraints were recognized as diam. and speed of rotation of the roller, number of cutters, diam. of the cutter and gap between the cutters. The numerical profile obtained from the method was in close agreement with experimental values. It was observed that, within the range of roller diam. and rotational speeds studied, (0.125-0.200 m and 1-2 m/min, respectively), the roller of diam. 0.165 m with 3 cutters was optimal, resulting in a max. output of 710 units/h, leaving about 38% scrap dough for recycling. [From En summ.]