







A calculus optimization problem 
20150514 

Ali pose la question : Given an elliptical piece of cardboard defined by (x^2)/4 + (y^2)/4 = 1. How much of the cardboard is wasted after the largest rectangle (that can be inscribed inside the ellipse) is cut out? Robert Dawson lui répond. 





A max min problem 
20120226 

Christy pose la question : Hello, I have no idea where to start with this question.
Bob is at point B, 35 miles from A. Alice is in a boat in the sea at point C, 3 miles from the beach. Alice rows at 2 miles per hour and walks at 4.25 miles per hour, where along the beach should she land so that she may get to Bob in the least amount of time? Penny Nom lui répond. 





Lost in the woods 
20120112 

Liz pose la question : I am lost in the woods. I believe that I am in the woods 3 miles from a straight road. My car is located 6 miles down the road. I can walk 2miles/hour in the woods and 4 miles/hour along the road. To minimize the time needed to walk to my car, what point on the road should i walk to? Harley Weston lui répond. 





Maximize the floor area 
20100707 

shirlyn pose la question : A rectangular building will be constructed on a lot in the form of a right triangle with legs
of 60 ft. and 80 ft. If the building has one side along the hypotenuse,
find its dimensions for maximum floor area. Penny Nom lui répond. 





An optimization problem 
20100523 

Marina pose la question : Hello, I have an optimization homework assignment and this question has me stumped..I don't even know A hiker finds herself in a forest 2 km from a long straight road. She wants to walk to her cabin 10 km away and also 2 km from the road. She can walk 8km/hr on the road but only 3km/hr in the forest. She decides to walk thru the forest to the road, along the road, and again thru the forest to her cabin. What angle theta would minimize the total time required for her to reach her cabin?
I'll do my best to copy the diagram here:
10km
Hiker_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Cabin
\  /
\  /
f \ 2km /
\  /
theta \___________________________ /
Road Penny Nom lui répond. 





Two max/min problems 
20100411 

Amanda pose la question : 1) Find the area of the largest isosceles triangle that canbe inscribed in a circle of radius 4 inches.
2)a solid is formed by adjoining two hemispheres to the end of a right circular cylinder. The total volume of the solid is 12 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. Tyler Wood lui répond. 





A maximum area problem 
20090113 

Kylie pose la question : Help me please! I don't know how or where to start and how to finish.
The problem is: A window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 15 ft., find the dimensions that will allow the maximum amount of light to enter. Harley Weston lui répond. 





Taxes in Taxylvania 
20081022 

April pose la question : Taxylvania has a tax code that rewards charitable giving. If a person gives p% of his income to charity, that person pays (351.8p)% tax on the remaining money. For example, if a person gives 10% of his income to charity, he pays 17 % tax on the remaining money. If a person gives 19.44% of his income to charity, he pays no tax on the remaining money. A person does not receive a tax refund if he gives more than 19.44% of his income to charity. Count Taxula earns $27,000. What percentage of his income should he give to charity to maximize the money he has after taxes and charitable giving? Harley Weston lui répond. 





A lidless box with square ends 
20080428 

Chris pose la question : A lidless box with square ends is to be made from a thin sheet of metal. Determine the least area of the metal for which the volume of the box is 3.5m^3.
I did this question and my answer is 11.08m^2 is this correct? If no can you show how you got the correct answer. Stephen La Rocque and Harley Weston lui répond. 





Minimize the cost 
20080426 

A pose la question : A power line is to be constructed from the shore of a lake to an island that is 500 m away. The closest powerline ends 4km along the shore from the point on the shore closest to the island. If it costs 5 times as much to lay the powerline underwater as along the shore, how should the line be installed to minimize the cost? Stephen La Rocque lui répond. 





Optimization  carrying a pipe 
20070505 

A student pose la question : A steel pipe is taken to a 9ft wide corridor. At the end of the corridor there is a 90° turn, to a 6ft wide corridor. How long is the longest pipe than can be turned in this corner? Stephen La Rocque lui répond. 





What are the dimensions of the most economical container? 
20070104 

Ashely pose la question : A cylindrical container costs $2.00 per square foot for the sides and $3.00 a square foot for the top and bottom. The container must hold 100 cubic feet of material. What are the dimensions of the most economical container. Stephen La Rocque lui répond. 





Linear programming and optimization 
19990409 

Shams pose la question : What is Linear programming and optimization? Jack LeSage and Penny Nom lui répond. 

