A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Welolington is buiding a shed with a square base measuring x feet by x feet, and which is h feet high. He wants the volume of the shed to be 224 ft3. Concrete for the base costs $3 per ft2. The materials for each of the four sides cost $2 per ft2. The flat roof will cost $11 per ft2.
If Wellington wants to minimize cost, the the objective function in terms of x and h is:
C = .
The constraint equation in terms of x and h is:
224 = .
The dimensions which minimize cost are x = ft and h = ft.
The minimal cost to build the shed is $
 2 years ago
Welolington is buiding a shed with a square base measuring x feet by x feet, and which is h feet high. He wants the volume of the shed to be 224 ft3. Concrete for the base costs $3 per ft2. The materials for each of the four sides cost $2 per ft2. The flat roof will cost $11 per ft2. If Wellington wants to minimize cost, the the objective function in terms of x and h is: C = . The constraint equation in terms of x and h is: 224 = . The dimensions which minimize cost are x = ft and h = ft. The minimal cost to build the shed is $

This Question is Open

matricked
 2 years ago
Best ResponseYou've already chosen the best response.1224 =x^2 h and C = 3x^2 +2*4x *h +11x^2=14x^2 +8xh=14x^2 +8x *(224/X^2) C=14x^2 +1792/x for max or min dC/dx=0 or 28x 1792/x^2 =0 or 28x^31792=0 or x^3 =224

matricked
 2 years ago
Best ResponseYou've already chosen the best response.1sorry for my wrong calculation as 28x^31792=0 or x^3 64 =0 or x^3=4^3 hence x=4 hence at x=4 the cost may be min

matricked
 2 years ago
Best ResponseYou've already chosen the best response.1for checking we have d/dx(dC/dx) = 28 +2(1792/x^3) and at x=4 d/dx(dC/dx) >0 hence at x=4 C is min when x=4 h= 224/16 =14 and C=14(16) + 1792/16 =224 + 112 =336

matricked
 2 years ago
Best ResponseYou've already chosen the best response.1oops again wrong calc for C C=14(16) +1792/4 =224 + 448 =672 (neglect 336)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
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.