







Maximizing the area of a two lot region 
20160403 

From yousef: A man wishes to enclose two separate lots with 300m of fencing. One lot is a square and the other a rectangle whose length is twice its width. Find the dimensions of each lot if the total area is to be a minimum. Answered by Penny Nom. 





Maximizing the ticket revenue 
20141007 

From Allen: An airplane whose capacity is 100 passengers is to be chartered for a flight to Europe. The fare is to be $150 per person, if 60 people buy tickets. However, the airline agrees to reduce the fare for every passenger by $1 for each additional ticket sold. How many tickets should be sold to maximize the ticket revenue for this flight? Answered by Chris Fisher. 





The popcorn box problem 
20131107 

From Dave: We know that calculus can be used to maximise the volume of the tray created when cutting squares from 4corners of a sheet of card and then folding up.
What I want is to find the sizes of card that lead to integer solutions for the size of the cutout, the paper size must also be integer. EG 14,32 cutout 3 maximises volume as does 13,48 cutout 3.
I have done this in Excel but would like a general solution and one that does not involve multiples of the first occurence, as 16, 10 cutout 2 is a multiple of 8,5 cutout 1. Answered by Walter Whiteley. 





Maximize the volume of a cone 
20131009 

From Conlan: Hi I am dong calculus at school and I'm stumped by this question:
A cone has a slant length of 30cm. Calculate the height, h, of the cone
if the volume is to be a maximum.
If anyone can help me it would be greatly appreciated.
thanks. Answered by Penny Nom. 





A max/min problem 
20121214 

From bailey: A right angled triangle OPQ is drawn as shown where O is at (0,0).
P is a point on the parabola y = ax – x^2
and Q is on the xaxis.
Show that the maximum possible area for the triangle OPQ is (2a^3)/(27) Answered by Penny Nom. 





A maximization problem 
20120409 

From Nancy: After an injection, the concentration of drug in a muscle varies according to a function of time, f(t). Suppose that t is measured in hours and f(t)=e^0.02t  e^0.42t. Determine the time when the maximum concentration of drug occurs. Answered by Penny Nom. 





A spherical ball in a conical wine glass 
20111026 

From Jules: A heavy spherical ball is lowered carefully into a full conical wine
glass whose depth is h and whose generating angle (between the axis
and a generator) is w. Show that the greatest overflow occurs when the
radius of the ball is (h*sin(w))/(sin(w)+cos(2w)). Answered by Claude Tardif. 





What is the maximum weekly profit? 
20101010 

From Joe: A local artist sells her portraits at the Eaton Mall.
Each portrait sells for $20 and she sells an average of 30 per week.
In order to increase her revenue, she wants to raise her price.
But she will lose one sale for every dollar increase in price.
If expenses are $10 per portrait, what price should be set to maximize the weekly profits?
What is the maximum weekly profit? Answered by Stephen La Rocque and Penny Nom. 





Maximizing the volume of a cylinder 
20100831 

From Haris: question: the cylinder below is to be made with 3000cm^2 of sheet metal. the aim of this assignment is to determine the dimensions (r and h) that would give the maximum volume.
how do i do this?
i have no idea. can you please send me a steptostep guide on how t do this?
thank you very much. Answered by Penny Nom. 





A max min problem 
20100819 

From Mark: a rectangular field is to be enclosed and divided into four equal lots by fences parallel to one of the side. A total of 10000 meters of fence are available .Find the area of the largest field that can be enclosed. Answered by Penny Nom. 





Maximize the floor area 
20100707 

From shirlyn: 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. Answered by Penny Nom. 





A max min problem 
20100406 

From Terry: The vertex of a right circular cone and the circular edge of its base lie on the surface of a sphere with a radius of 2m. Find the dimensions of the cone of maximum volume that can be inscribed in the sphere. Answered by Harley Weston. 





Maximizing the area of a rectangle 
20091217 

From rachel: A rectangular field is to be enclosed by 400m of fence. What dimensions will give a maximum area? Answered by Penny Nom. 





Maximize profit 
20091114 

From Willie: Profit is the difference between Total Revenue and Total Cost.
Therefore, to MAXIMIZE PROFIT you must maximize Total Revenue.
True or False? Explain answer. Answered by Penny Nom. 





A rectangular pen 
20090813 

From Kari: A rectangular pen is to be built using a total of 800 ft of fencing. Part of this fencing will be used
to build a fence across the middle of the rectangle (the rectangle is 2 squares fused together so if you can
please picture it).
Find the length and width that will give a rectangle with maximum total area. Answered by Stephen La Rocque. 

