You have to cut four equal squares from each corner of the 8.5" x 11" paper in order to make an open top box of maximum volume. Using optimization techniques, solve for the square cut outs.

Find the dimensions of the rectangular corral producing the greatest enclosed area given 200 feet of fencing.

Solve the initial value problem  y" + y = 4x + 10sinx ; y(pi) = 0 , y'(pi) = 2

There is a 4 foot wide walkway around a pool. The length of the pool is two feet less than 3 times the width. Find the area of the walkway in terms of W.

A contractor orders 8 cubic yards of premixed cement, all of which is to be used to pour a patio that will be 4 inches thick. If the length of the patio isspecified to be twice the width, what will be the patio dimensions? (1 cubic yard = 27 cubic feet)

A 40 inch wire is to be cut. One piece is to be bent into the shape of a square, whereas the other piece is to be bent into the shape of a rectangle whose length is twice the width. Find the width of the rectangle that will minimize the total area. What is the width of the rectangle that will minimize the total area? inches (Round to the nearest tenth as needed.)

A shed has the shape of a rectangular prism. The area of the floor of the shed is 63 square feet. The length of the shed is 2 feet greater than the width. The height is 1 foot less than the width.What is the volume of the shed in cubic feet?