Tuesday

July 29, 2014

July 29, 2014

Posted by **Bob** on Thursday, November 4, 2010 at 9:13pm.

- calculus -
**MathMate**, Thursday, November 4, 2010 at 10:04pmSince the base is square, and the volume is constant, there is only one variable, such as the side of the base, x.

The height is therefore h=V/x².

The cost of the base is

Cb=C1*x²

Cost of the four sides is

Cs=C2*(4x*h)

Cost of the cover is

Cc=C3*x²

Total cost as a function of x

C(x)= C1*x²+C2*(4x*V/x²)+C3*x²

=(C1+C3)x²+ 4C2*V/x

Differentiate with respect to x and equation f'(x) to zero. Solve for x0 where the cost is maximum/minimum.

To find out if f(x0) is a maximum or minimum, calculate the second derivative and evaluate f"(x0). If f"(x0)>0, f(x0) is a minimum. If f"(x0)<0, f(x0) is a maximum.

- calculus -
**joe smith**, Friday, November 9, 2012 at 11:59am45

**Related Questions**

Algebra - 4. A shipping crate has a square base with sides of length x feet, and...

calculus - a rectangular box is to have a square base and a volume of 20 ft ...

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

calculus - a company is designing shipping crated and wants the volume of each ...

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

Calculus - A company is designing shipping crates and wants the volume of each ...

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. ...