Posted by diwas on Tuesday, November 13, 2012 at 10:06pm.
a cabinet will inclose a rectangular loud speaker system and will have an internal volume of 2.4 cubic feet. The height will be 1.5 times the width. What are the dimesnions of the enclosure that can be constructed at a minimum cost?
- math - Reiny, Tuesday, November 13, 2012 at 10:44pm
length --- x
width --- y
height ---- 1.5y
1.5xy^2 = 2.4
x = 2.4/(1.5y^2) = 8/(5y^2)
Assuming the cost is a function of the surface area (SA)
SA = 2xy + 2(1.5xy) + 2(1.5y^2)
= 2xy + 3xy + 3y^2
= 5y((8/(5y^2) + 3y^2
= 8/y + 3y^2
d(SA)/dy = -8/y^2 + 6y = 0 for a min of SA
8/y^2 = 6y
6y^3 = 8
y^3 = 8/6
y = 2/6^(1/3) = 1.1006.. = appr 1.1
1.5y = 1.65
x = 8/(5(1.1006..)^2) = 1.32
length = 1.32
width = 1.1
height = 1.65
check: V = 1.32x1.1x1.65 = appr 2.3958 , close to 2.4, not bad
Answer This Question
More Related Questions
- honors algebra - the volume V of a rectangular prism is given by V=lwh, where l ...
- algebra - I have a rectangular prism with a volume of 48 cubic feet and a height...
- math - The perimeter of a rectangular cattle enclosure is 400 feet. It is 40 ...
- 6th grade - rectangular prism: height 7 feet, width 4 feet and length 3 feet ...
- Algebra - Please help. I have tried many times to come up with something after ...
- Math- volume - What could be the length and width of a rectangular prism with a ...
- math - concrete can be purchased cubic yard. How much will it cost to pour a ...
- MATH - Grady has designed a wooden storage cabinet for his CD's amd DVd's. The ...
- geometry - a rectangular box is to be constructed with its length four times the...
- Math - A fence to a rectangular enclosure has a width w, which Is (5m) shorter ...