Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

Looking for something else?

Not the answer you are looking for? Search for more explanations.

- anonymous

A closed box with square base is to be built to house an ant colony. The bottom of the box and all four sides are to be made of material costing 1 dollar/sq ft, and the top is to be constructed of glass costing 5 dollar/sq ft. What are the dimensions of the box of greatest volume that can be constructed for 72 dollars?
NOTE: Let denote the length of the side of the base and denote the height of the box

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

Get your **free** account and access **expert** answers to this and **thousands** of other questions

- anonymous

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

i know how to do this but im having trouble coming to the correct answer

- anonymous

V = x^2 y ....... x = base
we also know that
72 = 5(x^2) + 4(xy) + x^2
72 = 6x^2 + 4xy
xy = (36 - 3x^2)/2
thus
V = x(36 - 3x^2)/2
get the derivative and set it to zero, the resulting x-value is the length of the base of the box with the greatest volume.

- anonymous

can you help me do that cuz im apparently not doing it right

Looking for something else?

Not the answer you are looking for? Search for more explanations.

- anonymous

Surface Area = 2 tops + 4 sides
Area of square = 2 * x² + 4 * xy
Total Cost: $5 *x² + $1* ( 4xy + x²) = $ 72
6 x² + 4xy = 72
=>Area: xy = (72 - 6x² ) / 4
= 18 - 1.5 x²
=> Volume: x ( xy) = 18x - 1.5 x³
Thus maximum Volume: V' = 18 - 4.5 x² = 0
=> x = 2 ft, y = 6 ft

Looking for something else?

Not the answer you are looking for? Search for more explanations.