Sunday

March 29, 2015

March 29, 2015

Posted by **Megan** on Tuesday, May 27, 2008 at 7:34pm.

- Math-Optimization -
**Reiny**, Tuesday, May 27, 2008 at 10:53pmHaving seen and done hundreds of this type of question, I am pretty sure that the base is a square.

Else you don't have enough information to solve the question.

let the side of the base be x

let its height be y

so (x^2)y = 200 ---> y = 200/x^2

Cost = 3 money units(base) + 1 money unit(4 sides) + 1 money unit(top)

Cost = 3x^2 + 4(xy) + x^2

C = 4x^2 + 4xy

= 4x^2 + 4x(200/x^2)

= 4x^2 + 800/x

C' = 8x - 800/x^2 = 0 for a min of C

8x = 800/x^2

x^3 = 100

x = 4.64 and y = 9.28

PS, if the volume had been 2000 m^3 we would have had nice integer values.

Are you sure you did not make a typo?

**Answer this Question**

**Related Questions**

Math-Geometry - The material for the base of a box will cost three times as much...

math - a woman wants to construct a box whose base length is twice the base ...

calculus - A rectangular box is to be constructed from two different materials. ...

math - can someone help me with this question. I am completely stuck. A box with...

math - A rectangular box is to have a square base and a volume of 30 ft3. The ...

math - A rectangular box is to have a square base and a volume of 50 ft3. The ...

Calculus - A rectangular box is to have a square base and a volume of 20 ft3. ...

calculus - A rectangular box is to have a square base and a volume of 50 ft3. ...

calculus - A rectangular box is to have a square base and a volume of 50 ft3. ...

calculus - A rectangular box is to have a square base and a volume of 50 ft3. ...