A company needs to produce a cylindrical can to hold water. It must have a volume of 500ml. The side of the can will cost 40$/m^2 to produce and the top and bottom of the can will cost 50$/m^2 to produce. Find the most economical dimensions.
2 answers
Find the compound interest and the compound amount of the following #2ooo at 4/2 % compounded annually for 7yr
since pi r^2 h = 500, h = 500/(pi r^2)
the cost function is
c = 40 * 2pi r h + 2*50*pi r^2
= 80 pi r (500/(pi r^2)) + 100 pi r^2
= 40000/r + 100 pi r^2
dc/dr = 200 pi r - 40000/r^2
= 200 (pi r^3 - 200)/r^2
dc/dr = 0 when pi r^3 = 200
the cost function is
c = 40 * 2pi r h + 2*50*pi r^2
= 80 pi r (500/(pi r^2)) + 100 pi r^2
= 40000/r + 100 pi r^2
dc/dr = 200 pi r - 40000/r^2
= 200 (pi r^3 - 200)/r^2
dc/dr = 0 when pi r^3 = 200
2 answers