# Solving Optimization Problems - Page 2

Questions

- How do you find the point on the curve #y=2x^2# closest to (2,1)?
- What dimensions would you need to make a glass cage with maximum volume if you have a piece of glass that is 14" by 72"?
- A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is minimum?
- How do you minimize and maximize #f(x,y)=ye^(2x)-ln(y/x)# constrained to #0<xy-y+x<1#?
- A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola #y=6-x^2#. What are the dimensions of such a rectangle with the greatest possible area? thanks for any help!?
- Solve this problem? It's so hard for me
- Can some one help with this one? I am new to derivatives.
- A right circular cylinder is inscribed in a cone with height 6m and radius 3m. How do you find the largest possible volume of such a cylinder?
- How do you minimize and maximize #f(x,y)=(x-y)/x^2# constrained to #xy=4#?
- Find two positive numbers that satisfy the given requirements. The sum of the first number squared and the second number is 60 and the product is a maximum?
- How do you minimize and maximize #f(x,y)=x^2+y^3# constrained to #0<x+3xy<4#?
- How do you find the points on the parabola #y = 6 - x^2# that are closest to the point (0,3)?
- What will the dimensions of the resulting cardboard box be if the company wants to maximize the volume and they start with a flat piece of square cardboard 20 feet per side, and then cut smaller squares out of each corner and fold up the sides to create the box?
- How do you find the dimensions of a rectangle whose area is 100 square meters and whose perimeter is a minimum?
- Functions 11 Word Problem?
- How do you minimize and maximize #f(x,y)=(2x-3y)^2-1/x^2# constrained to #1<yx^2+xy^2<3#?
- How do you minimize and maximize #f(x,y)=sin^2y/x+cos^2x/y# constrained to #1<yx^2+xy^2<16#?
- How do you maximize a window that consists of an open rectangle topped by a semicircle and is to have a perimeter of 288 inches?
- A rectangular page is to contain 16 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used?
- A long rectangular sheet of metal, 12cm wide, is to be made into a rain gutter by turning up two sides which make an angle of 120 degrees with the base. How many cm should be turned up to give the gutter its greatest capacity?