### Welcome to the Forum Archive!

Years of conversation fill a ton of digital pages, and we've kept all of it accessible to browse or copy over. Whether you're looking for reveal articles for older champions, or the first time that Rammus rolled into an "OK" thread, or anything in between, you can find it here. When you're finished, check out the boards to join in the latest League of Legends discussions.

### Help me with me Calculus Homework pls (Optimization)

TheTuanster

Senior Member

1. An open box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. Find the dimensions of the box of maximum volume if the material has dimensions 6x6 inches.

2. An open box is to be constructed from cardboard by cutting out squares of equal size in the corners and then folding up the sides. If the cardboard is 6x11 inches, determine the volume of the largest box which can be constructed.

I absolutely have no idea where to start.

Shyvana420

Senior Member

Quote:
TheTuanster:
1. An open box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. Find the dimensions of the box of maximum volume if the material has dimensions 6x6 inches.

2. An open box is to be constructed from cardboard by cutting out squares of equal size in the corners and then folding up the sides. If the cardboard is 6x11 inches, determine the volume of the largest box which can be constructed.

I absolutely have no idea where to start.

1. Karthus

2. Im pretty sure its still Karthus (let me double check my work)

yupp Karthus

Member

Quote:
TheTuanster:
1. An open box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. Find the dimensions of the box of maximum volume if the material has dimensions 6x6 inches.

2. An open box is to be constructed from cardboard by cutting out squares of equal size in the corners and then folding up the sides. If the cardboard is 6x11 inches, determine the volume of the largest box which can be constructed.

I absolutely have no idea where to start.

Always start this kind of problem by setting up a formula to work with.

For #1, the volume of the resulting cube is going to be (6-2x)^3 where x is the length of the cutout in inches. Work from there.

Edit: Actually that equation is completely wrong. Gimme a sec.

TheTuanster

Senior Member

Quote:
The Fatalii:
1. Karthus

2. Im pretty sure its still Karthus (let me double check my work)

yupp Karthus

Ok thankyou! I had no idea it was that simple.

Mafia Goat

Senior Member

im so dumb i literally stared at this and in my head said "yup a box, that's a good box"

Durp Purple

Member

Quote:
The Fatalii:
1. Karthus

2. Im pretty sure its still Karthus (let me double check my work)

yupp Karthus

Rofl

Sandageto

Senior Member

pay attention in class then retarded downie

calc was years ago for me and i can tell you it has to do with taking a derivative to find the max and min

Crastym

Senior Member

Let's see.... #2

V = (6-2z) * (11-2z) * z where z is the length of one of the sides of the square, which also happens to be the height of the box.

Take the derivative of V with respect to z, set dV equal to 0, then solve for z. You'll want to expand V before you take the derivative.

Let me know what you get?

True Vanity

Senior Member

Quote:
Always start this kind of problem by setting up a formula to work with.

For #1, the volume of the resulting cube is going to be (6-2x)^3 where x is the length of the cutout in inches. Work from there.

Edit: Actually that equation is completely wrong. Gimme a sec.

V = (L)(W)(H) = (6-2x)(6-2x)(x)