- Thread starter
- #1

answer H = 6R and R = cubic root of ( 3V/22pi)

Ok

V = 2pir

^{2}H+4/3pir

^{3}

The cost Function where i think it is my mistake is

C = 4pir

^{2}H +4pir

^{3}

- Thread starter leprofece
- Start date

- Thread starter
- #1

answer H = 6R and R = cubic root of ( 3V/22pi)

Ok

V = 2pir

The cost Function where i think it is my mistake is

C = 4pir

- Admin
- #2

I have no idea what you mean by " 'V' shaped geometric body torque limited cylindrical half-spheres." Is this in fact just a right circular cylinder capped at both ends by hemispheres? If so, you are making the same mistake you made in the boiler problem concerning the volume of this body.

I would let the cost per unit square of the sides of the cylindrical portion be $k$ (in whatever units of currency you choose). Then your cost function would be:

Total cost = k(area of cylindrical portion) + 2k(area of lower hemisphere) + 3k(area of upper hemisphere)

You should now be able to state your objective function and constraint. What do you find?

- Thread starter
- #3

Cost = k(4pirI have no idea what you mean by " 'V' shaped geometric body torque limited cylindrical half-spheres." Is this in fact just a right circular cylinder capped at both ends by hemispheres? If so, you are making the same mistake you made in the boiler problem concerning the volume of this body.

I would let the cost per unit square of the sides of the cylindrical portion be $k$ (in whatever units of currency you choose). Then your cost function would be:

Total cost = k(area of cylindrical portion) + 2k(area of lower hemisphere) + 3k(area of upper hemisphere)

You should now be able to state your objective function and constraint. What do you find?

This must be the cost equation

- Admin
- #4

No, what is the formula for the lateral surface of a cylinder? And why does your third term have factors of $2k$ and $3k$? Look at the formula I gave and carefully insert the correct area formulas.Cost = k(4pir_{2}·+2k(2/3pir^{3})+3k 2k(2/3pir^{3})

This must be the cost equation

- Thread starter
- #5

No, what is the formula for the lateral surface of a cylinder? And why does your third term have factors of $2k$ and $3k$? Look at the formula I gave and carefully insert the correct area formulas.

C= 2pirh+ 2pir

This?????

- Admin
- #6

\(\displaystyle C(r,h)=k(2\pi rh)+2k\left(2\pi r^2 \right)+3k\left(2\pi r^2 \right)=2k\pi r\left(h+5r \right)\)

Now, can you state the constraint, and solve it for $h$ so that you will be able to express the objective function in terms of just the variable $r$?

- Thread starter
- #7

Ok is it ????

\(\displaystyle C(r,h)=k(2\pi rh)+2k\left(2\pi r^2 \right)+3k\left(2\pi r^2 \right)=2k\pi r\left(h+5r \right)\)

Now, can you state the constraint, and solve it for $h$ so that you will be able to express the objective function in terms of just the variable $r$?

V = 2pir2H+4/3pir3

- Admin
- #8

If I am reading this correctly as:Ok is it ????

V = 2pir2H+4/3pir3

\(\displaystyle V=2\pi r^2h+\frac{4}{3}\pi r^3\)

then no, that does not described the volume of the body. You have made this same error three times now.

You want:

\(\displaystyle V=\pi r^2h+\frac{4}{3}\pi r^3\)

Recall that the volume of a cylinder is $\pi r^2h$. Now, solve this constraint for $h$ and then substitute for $h$ into the cost function, and then minimize.