# Solving Optimization Problems - Page 4

Questions

- How do you minimize and maximize #f(x,y)=xe^x-y# constrained to #0<x-y<1#?
- A physical fitness room consists of a rectangular region with a semicircle on each end. If the perimeter of the room is to be a 200 meter running track, how do find the dimensions that will make the area of the rectangular regions as large as possible?
- How do you find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2?
- How do you minimize and maximize #f(x,y)=(x-y)/(x^3-y^3# constrained to #2<xy<4#?
- How do you minimize and maximize #f(x,y)=(x^2+4y)/e^(y)# constrained to #0<x-y<1#?
- How do you find the cost of materials for the cheapest such container given a rectangular storage container with an open top is to have a volume of #10m^3# and the length of its base is twice the width, and the base costs $10 per square meter and material for the sides costs $6 per square meter?
- What is the smallest possible value of the sum of their squares if the sum of two positive numbers is 16?
- What is the maximum possible area of the rectangle that is to be inscribed in a semicircle of radius 8?
- How do you minimize and maximize #f(x,y)=x^2+y^3# constrained to #0<x+3y<2#?
- How do you minimize and maximize #f(x,y)=e^x/e^y-x^2y# constrained to #0<xy+y^2<1#?
- Can anybody help me with this optimization problem?
- How do you find the volume of the largest open box that can be made from a piece of cardboard 35 inches by 19 inches by cutting equal squares from the corners and turning up the sides?
- A cylinder is inscribed in a right circular cone of height 6 and radius (at the base) equal to 5. What are the dimensions of such a cylinder which has maximum volume?
- How do you minimize and maximize #f(x,y)=(2x-y)+(x-2y)/x^2# constrained to #1<yx^2+xy^2<3#?
- How do you find two positive numbers whose product is 750 and for which the sum of one and 10 times the other is a minimum?
- An open -top box is to be made by cutting small congruent squares from the corners of a 12-by12-in. sheet of tin and bending up the sides. How large should the squares cut from the corners be to make the box hold as much as possible?
- A sodium chloride crystal in the shape of a cube is expanding at the rate of 60 cubic microns per second. How fast is the side of the cube growing when the volume is 1000 cubic microns?
- What is the largest area that can be fenced off of a rectangular garden if it will be fenced off with 220 feet of available material?
- Stevie completes a quest by travelling from #A# to #C# vi #P#. The speed along #AP# is 4 km/hour, and along #AB# it is 5 km/hour. Solve the following?
- A steel girder is taken to a 15ft wide corridor. At the end of the corridor there is a 90° turn, to a 9ft wide corridor. How long is the longest girder than can be turned in this corner?