Find the Global Maximum

Maximize the product of two numbers, x and y, given that the first number squared added to the second number is equal to 27.

A dudebro has 500 feet of fencing to make a pig pen along a barn as shown below. Find the maximum area.

A rectangle has a perimeter of 40 feet. Find the width and height of a rectangle with a maximum area.

A company makes wrenches. It costs them an initial \$10,000 to set up and an additional \$5.00 for each wrench. A market study indicates that if the price of a wrench is \$5.00 then the company will sell 200,000 wrenches. However, for every \$10 that the company raises the price per wrench, only half as many people will buy the wrench. What price should they charge per wrench to maximize the companies profits.