K* v2 +6v+6 (4.58) It is easy to show that the solution, vopt, of this equation satisfies the inequality < v,,pt < #.7 + 1. Consequently, when Al/K" is large, the optimum v is v°P1— Thus, for Al/K" large, we obtain -) =1+2 K — M (4.59) (4.60) Figure S1 shows the critical benefit-to-cost ra