Generalize the results of Prob. 17–31 by representing the factor of safety n as

n = ad/(b/m) + cd2

Where m is the number of ropes supporting the cage, and a, b, and c are constants. Show that the optimal diameter is d* = [b/(mc)]1/2 and the corresponding maximum attainable factor of safety is n* = a[m/(bc)]1/2/2.