Choosing the draft length

With acceptance rate $\alpha$ and relative draft cost $c$, speedup is $\mathcal S(\gamma) = (1-\alpha^{\gamma+1})/\big((1-\alpha)(\gamma c+1)\big)$.

1. For $\alpha = 0.7$, $c = 0.15$, tabulate $\mathcal S$ for $\gamma = 1,\dots,8$ and find the optimum.
2. Show that as $c \to 0$ the optimal $\gamma$ diverges, and give the limiting speedup for fixed $\gamma \to\infty$.
3. A team reports $\alpha = 0.95$ and claims a $10\times$ speedup. Is that consistent?