1. Optimization Problems 1.Identify the quantity you’re optimizing 2.Write an equation for that quantity 3.Identify any constraints, and use them to get the equation in step 2 in terms of one variable 4.Now take the derivative of the equation 3 and find any critical numbers 5.Use the critical numbers to locate where there is a maximum or minimum 6.Use the info from 5 to solve for what as asked (don’t forget units!) Find dimensions of a rectangle w/ area 1000 m^2 whose perimeter is as small as possible.

2. Farmer Joe needs to enclose a field for his horses. He has 500 feet of fencing and plans to build a rectangular pen where one side of the field is bordered by a river (and thus does not require fencing). Find the maximum area for Joe’s horse field.

3. An open-top cylindrical tank with a volume of ten cubic feet is to be made from a sheet of steel. Find the dimensions of the tank that will require as little material used in the tank as possible.