Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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
 2 years ago
 2 years ago
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
 2 years ago
 2 years ago

This Question is Closed

m.auld64Best ResponseYou've already chosen the best response.0
i know how to do this but im having trouble coming to the correct answer
 2 years ago

kumar2006Best ResponseYou've already chosen the best response.1
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 xvalue is the length of the base of the box with the greatest volume.
 2 years ago

m.auld64Best ResponseYou've already chosen the best response.0
can you help me do that cuz im apparently not doing it right
 2 years ago

ChlorophyllBest ResponseYou've already chosen the best response.0
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
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.