A rectangular garden is to be constructed using a rock wall as one side of the garden and wire fencing for the three other sides. Given 100 meters of wire fencing determine the dimensions that would create a garden of maximum area. What is the maximum area?
An open top box is to be made from a 24 meters by 36 meters piece of cardboard by removing a square from each corner of the cardboard and folding the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume? What is the maximum volume?
A rectangular box with square base, an open top and volume of 216 cubic meters is to be constructed. What should be the dimensions of the box to minimize the surface area of the box? What is the minimum surface area?
An island is two kilometers due north of its closest point along a straight shoreline. A visitor is staying at a cabin on the shore that is six kilometer west of that point. The visitor is planning to go from the cabin to the island. Suppose the visitor runs at a rate of 8 km/h and swims at a rate of 3 km/h. How far should the visitor run before swimming to minimize the time it takes to reach the island?
A rectangle is inscribed inside the ellipse with equation
What should be the dimensions of the rectangle to maximize its area? What is the maximum area?
Car rental company has determined that if they charge customers dollars per day to rent a car, where , the number of rented cars can be modeled by the function
If rental fee is less than 50 dollars per day, all cars will be rented. If the fee is more that 200 dollars per day, no cars will be rented. Assuming company plans to charge between 50 and 200 dollars per day, which fee maximizes revenue?