1. The "gait" of an animal is a measure of how jerky or smooth the animal's motion appers when it is running. Gait, g can be shown to be related to the power, P, necessary for the animal to run at a given speed. For an animal 1m long, running at a velocity of 10m/s, the power is given by
P= 0.1g + 1000/1+g.
Determine the gait that minimizes the required power for the animal to run.
2. Jeff is making a toy box for his nephew. He will use pine for the square base and sides. but oak for the top. Pine costs $16/m squared and oak costs $20/m squared. If the volume of the toy box is to be 1.3 m cubed, fined the amount of oak that is needed if the cost of all the wood for the toy box is to be as low as possible.