
Optimization
How would one go about approaching the following problems...
Find the area of the largest rectangle that can be inscribed in a right triangle with legs of 3cm and 4cm if 2 sides of the rectangle lie along the sides of the triangle.
A store owner finds that he can sell 30 sets of golf clubs at $500 per set in a year. furthermore, he predicts that for each $25 decrease in price, she could sell three extra sets of golf clubs. At what price should she sell the clubs to maximize gross income?
Thanks a bunch!