# Solving Optimization Problems - Page 5

Questions

- An open-top box with a square base has a surface area of 1200 square inches. How do you find the largest possible volume of the box?
- A rectangular sheet with perimeter of 33cm and dimensions x by y are rolled into a cylinder, x being the perimeter What values x and y give the largest volume?
- Let's say I have $480 to fence in a rectangular garden. The fencing for the north and south sides of the garden costs $10 per foot and the fencing for the east and west sides costs $15 per foot. How can I find the dimensions of the largest possible garden.?
- How do you minimize and maximize #f(x,y)=x-y/(x-y/(x-y))# constrained to #1<yx^2+xy^2<16#?
- How do you maximize and minimize #f(x,y)=e^-x+e^(-3y)-xy# subject to #x+2y<7#?
- A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. How can he do this so as to minimize the cost of the fence?
- How do you find the dimensions of a rectangle with area 1000 m whose perimeter is as small as possible?
- How do you find the points on the ellipse #4x^2+y^2=4# that are farthest from the point #(1,0)#?
- Find the length and width of a rectangle that has the given perimeter and a maximum area? Perimeter: 164 meters
- How do you minimize and maximize #f(x,y)=(x-y)/(x^2+y^2)# constrained to #0<xy-y^2<5#?
- How do you minimize and maximize #f(x,y)=(e^(yx)-e^(-yx))/(2yx)# constrained to #1<x^2/y+y^2/x<3#?
- How do you find the point on the line #y=4x + 7# that is closest to the point (0,-3)?
- A rectangle is constructed with it's base on the x-axis and the two of its vertices on the parabola #y=49 - x^2#. What are the dimensions of the rectangle with the maximum area?
- The top and bottom margins of a poster are 4 cm and the side margins are each 6 cm. If the area of printed material on the poster is fixed at 384 square centimeters, how do you find the dimensions of the poster with the smallest area?
- A right cylinder is inscribed in a sphere of radius r. How do you find the largest possible volume of such a cylinder?
- How do you find the dimensions of a rectangular box that has the largest volume and surface area of 56 square units?
- A rectangle with sides parallel to the axes is inscribed in the region bounded by the axes and the line x+2y = 2. How do you find the maximum area of this triangle?
- .There was a proposal for the new size of the advisory boards to be placed at strategic locations along the expressway. The board must contain 50 square meters of print and margins of 4 meters at the top and bottom while 3 meters on each side.?
- A square and a equilateral triangle are to be formed out of the same piece of wire. The wire is 6 inches long. How do you maximize the total area the square and the triangle contain?
- If 2400 square centimeters of material is available to make a box with a square base and an open top, how do you find the largest possible volume of the box?