







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. 





A cone circumscribed about a given hemisphere 
20100119 

Neven pose la question : The cone of smallest possible volume is circumscribed about a given hemisphere. What is the ratio of its height to the diameter of its base?
(G.F.Simmons, Calculus with Analytic Geometry, CH4 Applications of Derivatives) Chris Fisher lui répond. 





Ordering pizza for 162 people 
20091001 

Jean pose la question : Need to know how to feed about 162 people 70 square inches of pizza at the lowest price.
22" Pizza is $9.95
16" Pizza is $5.25
12" Pizza is $2.99 Penny Nom lui répond. 





A kennel with 3 individual pens 
20090106 

Jean pose la question : An animal clinic wants to construct a kennel with 3 individual pens, each with a gate 4 feet wide and an area of 90 square feet. The fencing does not include the gates.
Write a function to express the fencing as a function of x.
Find the dimensions for each pen, to the nearest tenth of a foot that would produce the required area of 90 square feet but would use the least fencing. What is the minimum fencing to the nearest tenth? Harley Weston lui répond. 





How many presses should be used? 
20080504 

Sarah pose la question : Hi! I am in Calculus and this problem is on my study guide and i just cant figure it out!?
A printing company had eight presses, each of which can print 300 copies per hour. It costs $5.00 to set up each press for a run and 12.5+6n dollars to run n presses for an hour. How many presses should be used to print 6000 copies most profitably? Let h equal the number of hours used to print the 6000 copies. 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. 





A maxmin problem 
20080327 

LSL pose la question : show that of all rectangle with a given area, the square has the smallest perimeter. Penny Nom lui répond. 





Protecting a carrot patch 
20080103 

Kate pose la question : A farmer has a problem with rabbits and skunks
in his rectangular carrot patch that is 21m^2 in area. Determine the
dimensions that will require the least amount of fencing if a barn can
be used to protect one side of the garden. Stephen La Rocque lui répond. 





Minimum cost for a fixed volume 
20070418 

James pose la question : My question goes: A silo is to be constructed and surmounted by a hemisphere. The material of the hemisphere cost twice as much as the walls of the silo. Determine the dimensions to be used of cost is to be kept to a minimum and the volume is fixed. Penny Nom lui répond. 





Minimizing a cost 
20060725 

Edward pose la question : The cost of running a car at an average speed of V km/h is given by c= 100 + (V2 / 75) cents per hour. Find the average speed (to the nearest km/h) at which the cost of a 1000 km trip is a minimum. Stephen La Rocque lui répond. 





Maximizing the angle to the goal mouth 
20040515 

Yogendra pose la question : You are running down the boundary line dribbling the ball in soccer or hockey. Investigate where in your run the angle the goal mouth makes with your position is at a maximum. Penny Nom lui répond. 





Getting to B in the shortest time 
20011219 

Nancy pose la question : A motorist in a desert 5 mi. from point A, which is the nearest point on a long, straight road, wishes to get to point B on the road. If the car can travel 15 mi/hr on the desert and 39 mi/hr on the road to get to B, in the shortest possible time if...... A.) B is 5 mi. from A B.) B is 10 mi. from A C.) B is 1 mi. from A Penny Nom lui répond. 





A lighthouse problem 
20011102 

A student pose la question : A lighthouse at apoint P is 3 miles offshore from the nearest point O of a straight beach. A store is located 5 miles down the beach from O. The lighthouse keeper can row at 4 mph and walk at 3.25 mph.
a)How far doen the beach from O should the lighthouse keeper land in order to minimize the time from the lighthouse to the store?
b)What is the minimum rowing speed the makes it faster to row all the way? Harley Weston lui répond. 





A problem with a quadratic 
20000809 

David Xiao pose la question : Find the value of a such that 4x^{2} + 4(a2)x  8a^{2} + 14a + 31 = 0 has real roots whose sum of squares is minimum. Harley Weston lui répond. 





Minimizing the metal in a can 
20000502 

May Thin Zar Han pose la question : A can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. Harley Weston lui répond. 

