anonymous
  • 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
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
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 this expert

answer on brainly

SEE EXPERT ANSWER

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

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

More answers

anonymous
  • 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.