Chapter 4.3, Problem 44E

A bird such as a starling feeds worms to its young. To collect worms, the bird flies to a site where worms are to be found, picks up several in its beak, and flies back to its nest. The loading curve in Figure 4.45 shows how the number of worms (the load) a starling collects depends on the time it has been searching for them.⁴ The curve is concave down because the bird can pick up worms more efficiently when its beak is empty; when its beak is partly full, the bird becomes much less efficient. The traveling time (from nest to site and back) is represented by the distance PO in Figure 4.45. The bird wants to maximize the rate at which it brings worms to the nest, where

$\mathrm{Rate}wormsarrive=\frac{Load}{Travelingtime+Searchingtime}$

Figure 4.45