Pre Calculus

posted by Joey

A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides
of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be
thicker, and costs 0.06 cents per square centimeter. Find the dimensions for the can that will minimize
production cost.

Height of the can:

Minimum cost:

1. Steve

πr^2h = 200, so h = 200/πr^2

The cost is thus

c = .02*2πrh + .06*2πr^2
= .04πr(200/πr^2) + .12πr^2
= 8/r + .12πr^2

dc/dr = -8/r^2 + .24πr
dc/dr=0 when r ≈ 2.2

Now just crank out h and c

Similar Questions

1. Calculus

A right cicular cylindrical can is to be constructed to have a volume of 57.749 cubic inches (one quart). The sides of the can are to be formed by rolling and welding a strip of metal, which may be purchased in rolls with width equal …
2. math

A right cicular cylindrical can is to be constructed to have a volume of 57.749 cubic inches (one quart). The sides of the can are to be formed by rolling and welding a strip of metal, which may be purchased in rolls with width equal …
3. calculus

A rectangular box is to be constructed from two different materials. The box will have a square base and open top. The material for the bottom costs \$4.25/m2. The material for the sides costs \$2.50/m2. Find the dimensions of the box …
4. Math

A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and …
5. Math (algebra)

Could you help me with this math question: A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs 11 cents per square centimeter, while …
6. math algebra

Can someone help me with this question? A can in the shape of a right circular cylinder is required to have a volume of 1,000 cubic centimeters. The top and bottom are made up of a material that costs 10ยข per square centimeter, while
7. Calculus

A box with square base and rectangular sides is being designed. The material for the sides costs 20 cents per square inch and that for the too and bottom costs 10 cents per square inch. The box is to hold 150 cubic inches. What dimension …
8. math

A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 550 cubic centimeters of soup. The sides and bottom of the container will be made of syrofoam costing 0.03 cents per square centimeter. The …
9. Pre calc

A cylinder shaped can needs to be constructed to hold 1000 cubic centimeters of soup. The material for the sides of the can costs 0.1 cents per square centimeter. The material for the top is.2 and the bottom is .3 cents per square …
10. help meee

A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and …

More Similar Questions