







Lost in the woods 
20120112 

From Liz: 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? Answered by Harley Weston. 





A cone circumscribed about a given hemisphere 
20100119 

From Neven: 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) Answered by Chris Fisher. 





Ordering pizza for 162 people 
20091001 

From Jean: 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 Answered by Penny Nom. 





A kennel with 3 individual pens 
20090106 

From Jean: 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? Answered by Harley Weston. 





How many presses should be used? 
20080504 

From Sarah: 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. Answered by Harley Weston. 





A lidless box with square ends 
20080428 

From Chris: 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. Answered by Stephen La Rocque and Harley Weston. 





Minimize the cost 
20080426 

From A: 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? Answered by Stephen La Rocque. 





A maxmin problem 
20080327 

From LSL: show that of all rectangle with a given area, the square has the smallest perimeter. Answered by Penny Nom. 





Protecting a carrot patch 
20080103 

From Kate: 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. Answered by Stephen La Rocque. 





Minimum cost for a fixed volume 
20070418 

From James: 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. Answered by Penny Nom. 





Minimizing a cost 
20060725 

From Edward: 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. Answered by Stephen La Rocque. 





Maximizing the angle to the goal mouth 
20040515 

From Yogendra: 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. Answered by Penny Nom. 





Getting to B in the shortest time 
20011219 

From Nancy: 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 Answered by Penny Nom. 





A lighthouse problem 
20011102 

From A student: 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? Answered by Harley Weston. 





A problem with a quadratic 
20000809 

From David Xiao: 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. Answered by Harley Weston. 





Minimizing the metal in a can 
20000502 

From May Thin Zar Han: 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. Answered by Harley Weston. 

