Solved: A bird such as a starling feeds worms to its young. To collect worms, the bird

Chapter 4, Problem 41

(choose chapter or problem)

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 4.42 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 P O in Figure 4.42. The bird wants to maximize the rate at which it brings worms to the nest, where Rate worms arrive = Load Traveling time + Searching time (a) Draw a line in Figure 4.42 whose slope is this rate. (b) Using the graph, estimate the load which maximizes this rate. (c) If the traveling time is increased, does the optimal load increase or decrease? Why? O P 4 8 time load (number of worms) Number of worms Traveling time Searching ti