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	Taxes in Taxylvania		2008-10-22
		From April: Taxylvania has a tax code that rewards charitable giving. If a person gives p% of his income to charity, that person pays (35-1.8p)% 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? Answered by Harley Weston.
	Maximize revenue		2008-10-08
		From Donna: A university is trying to determine what price to charge for football tickets. At a price of 6.oo/ticket it averages 70000 people per game. For every 1.oo increase in price, it loses 10000 people from the average attendance. Each person on average spends 1.5o on concessions. What ticket price should be charged in order to maximize revenue. price = 6+x, x is the number of increases. ticket sales = 70000- 10000x concession revenue 1.5(70000 - 10000x) I just do not know what to do with the concession part of this equation (6+x) x (70000 - 10000x) I can understand but not the concession part please help. thx. Answered by Penny Nom.
	The isoperimetric inequality		2008-04-21
		From Dutch: I'm searching for the proof that the sphere has the smallest volume of any figure and maximizes the volume of any figure. Answered by Chris Fisher.
	A quadratic function word problem		2007-11-12
		From liz: A kernal of popcorn contains water that expands when the kernal is heated, causing it to pop. The equations below give the "popping volume"y(in cubic centimeters per gram) of popcorn with moisture content x(as a percent of the popcorn's weight). hot air popping: y = -0.761x^2 + 21.4x-94.8 hot oil popping: y = -0.652x^2 + 17.7x -76.0 A) for hot air popping, what moisture content maximizes popping volume? What is the maximum volume? B) For hot oil popping, what mositure content maximizes popping volume? What is the maximum volume? C) the moisture content of popcorn tyipcally ranges from 8% to 18%. Graph the equations for hot air and hot oil popping on the interval 8 less then or equal to x and less then or equal to 18. D) Based on the graphs from part(c), what general statement can you make about the volume of popcorn produced from hot air popping verus hot oil popping for any moisture content in the interval8 less then or equal to x and less then or equal to 18. Answered by Penny Nom.
	The range of a projectile		2007-09-18
		From Claudette: This is a maximum minimum problem that my textbook didn't even try to give an example of how to do it in the text itself. It just suddenly appears in the exercises. Problem: The range of a projectile is R = v^2 Sin 2x/g, where v is its initial velocity, g is the acceleration due to gravity and is a constant, and x is the firing angle. Find the angle that maximizes the projectile's range. The author gives no information other than the formula. I thought to find the derivative of the formula setting that to zero, but once I had done that, I still had nothing that addressed the author's question. Any help would be sincerely appreciated. Claudette Answered by Stephen La Rocque.
	Maximize the volume of a cone		2007-04-27
		From ashley: hello, I've been stumped for hours on this problem and can't quite figure it out. The question is: A tepee is a cone-shaped shelter with no bottom. Suppose you have 200 square feet of canvas (shaped however you like) to make a tepee. Use calculus to find the height and radius of such a tepee that encloses the biggest volume. Can you help?? Answered by Stephen La Rocque and Penny Nom.
	Linear programming		2002-05-27
		From Jes: A machine shop makes two parts, I and II, each requiring the use of three machines, A, B, C. Each Part I requires 4 minutes on Machine A, four minutes on Machine B and five minutes on machine C. Each Part II requires five minutes on Machine A, one minutes on Machine B and six minutes on Machine C. The shop makes a profit of $8 on each Part I and $5 on each Part II. However, the number of units of Part II produced must not be less than half the number of Part I. Also each day the shop has only 120 minutes of machine A, 72 minutes of Machine B, and 180 minutes of Machine C available for the production of the two parts. What should be the daily production of each part to maximize the shop's profit? Answered by Claude Tardif.
	The city transit system		2001-01-07
		From Jacky: The city transit system carries an average of 9450 bus riders a day, for a fare of $1.75 each. The city wants to reduce car pollution by increasing ridership and to maximize the transit system's revenue at the same time. A survey indicates that the number of riders will increase by 150 for every $0.05 decrease in fare. Answered by Harley Weston.
	An integer max-min problem		2000-03-13
		From Paul Servic: Maximize Q = xy 2 where x and y are positive integers such that x + y 2 = 4 Answered by Penny Nom.

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