A soup can in the shape of a right circular cylinder is to be made from two materials. The material for the "sides" costs $.015 per square inch and the material for the two "lids" costs $.027 per square inch. The can must have a volume of 16 cubic inches. Find the dimensions of the can that minimize the cost of the can.
Do I just minimize the amount of material or is there someway I have to take into consideration the costs when finding the dimensions? What is your answer?
2006-11-12 16:11:34 · 3 answers · asked by ben_ev0lent 1 in Science & Mathematics ➔ Mathematics
It is my understanding that you would multiply the given costs by the surface area of those pieces to get total cost (C). Your equation would be as follows:
2[(πr^2)(.027)] x πrh(.015)=C
The constraint equation is the volume:
(πhr^2) = 16
solve your constraint equation for one of the variables.
Then take the derivative of the cost equation and solve for your variable at "0." This will give you r (where r is radius) or h (where h is height of can) depending on what you solved for.
2006-11-15 02:55:39 · answer #1 · answered by L P 1 · 0⤊ 0⤋
You have two equations, one for the cost and the other for the volume. Since the volume is fixed, the height and radius are inversely related, which means you can substitute for either the height or the volume in the area equation, allowing you to minimize the overall cost with a single variable.
2006-11-12 16:15:45 · answer #2 · answered by arbiter007 6 · 0⤊ 0⤋
Boo! no one cares about what kind of high school math you took.
I bet when you learn something more advanced you'll copy a question from your textbook and ask it on this website.
Actually I'm rather lazy and prefer not to work that problem out... I'm sure differentiating and integrating and all that nonsense are not that hard for you
2006-11-12 16:18:18 · answer #3 · answered by Daniel C 4 · 0⤊ 0⤋