Question

Let’s now complete the “open box” question mentioned in the previous question. Suppose we have 1200in2 of material that we will use to create a box that has a rectangular base (the base may or may not be a square), but no top. What dimensions maximize the volume?

(a) Draw a sketch of the box in this question. Appropriately label the relevant information in your sketch.

(b) Based on your sketch above, what equation is being maximized?

(c) Based on your sketch above, what equation represents the given constraint?

(d) If we also know that the base is a square, find the dimensions of the box that gives the largest volume.

(e) How much material is used on the base? How much material is used on the sides? Do you notice anything about the amount of material used on the sides compared to the base? What about the right/left, the front/back, and the base? Depending on your labeling, this might be 2*width*height, 2*length*height and length*width (the first two are multiplied by 2, representing the two sides with those dimensions).

(f) Does your conjecture in the previous question need any revision? If so, make a revised conjecture.

Answer 1