Chapter P.4, Problem 95E

Sailboat Races The speed that a sailboat is capable of sailing is determined by three factors: its total length L, the surface area A of its sails, and its displacement V (the volume of water it displaces).

In general, a sailboat is capable of greater speed if it is longer, has a larger sail area, or displaces less water. To make sailing races fair, only boat in the same “class” can qualify to race together. For a certain race, a boat is considered to qualify if $0.30L+0.38A^{1/2}-3V^{1/3}\le 16$

Where L is measured in feet, A in square feet, and V in cubic feet. Use this inequality to answer the following questions.
(a) A sailboat has length $60\text{ft}$ , sail area $3400{\text{ft}}^2$ ,and displacement $650{\text{ft}}^3$ . Does this boat qualify for the race?
(b) A sailboat has length $65\text{ft}$ and displace $600{\text{ft}}^3$ . What is the largest possible sail area that could be used and still allow the boat to qualify for this race?