Optimizing Load per Time

Bird Feeding

We have a bird searching for food to bring back to its young. The blue distance from A to B represents the amount of time it take to get to the nest to the hunting grounds and back again. The purple distance (x-coordinate of C) is the amount of time spent searching for food. The y-coordinate of C is the amount of food found to be brought back to the nest. The bird wants to minimize the amount of food brought back per time.

Visualizing the Rate

How can we graphically represent the amount of food brought back per time?

Graphically Finding the Optimal Position

Manipulate the position of C to find the optimal position. What can we say about the red line at this point?