Posted by Caitlin on Tuesday, June 5, 2012 at 8:53pm.
A closed box with a square base is to be constructed so that its volume is 324 cubed feet. The material for the top and bottom cost is $3 per square foot, and that for the sides $2 per square foot. Find the dimensions of the box so that the cost will be minimum.
- Calc - Damon, Tuesday, June 5, 2012 at 9:01pm
top and bottom are w by w
height is h
324 = w^2 h so h = 324/w^2
Cost = 6 w^2 + 4 w h
= 6 w^2 + 4 w (324/w^2)
= 6 w^2 + 1296/w
dC/dw = 0 for min = 12 w -1296/w^2
0 = 12 w^3 - 1296
w^3 = 108
w = 4.76
h = 14.3
- Calc - Caitlin, Tuesday, June 5, 2012 at 9:10pm
Are you sure about the 4w (324/w^2)?
Shouldn't it be 8w (324/w^2), since you are multiplying the four sides by the cost of $2 per square foot?
- Calc - MathMate, Tuesday, June 5, 2012 at 10:21pm
Yes, you're right.
If we proceed with
Cost = 6 w^2 + 8 w h
w=6 and h=9.
Answer this Question
More Related Questions
- Math - A rectangular box is to have a square base and volume of 78 feet cubed. ...
- Calculus - dimensions of a box? - A rectangular box with a square bottom and a ...
- Calculus - A rectangular box is to have a square base and a volume of 20 ft3. If...
- CALC - An open box is to be constructed so that the length of the base is 4 ...
- Calculus - A box is constructed out of two different types of metal. The metal ...
- calculus - A box is constructed out of two different types of metal. The metal ...
- Algebra - 4. A shipping crate has a square base with sides of length x feet, and...
- Calculus - A rectangular box with square base (which is NOT necessarily a cube) ...
- calculus - a rectangular box is to have a square base and a volume of 20 ft ...
- Calculus I - An open box with square base is to be constructed. The material for...