Optimisation problem- can anyone help?

[Robins]

A rectangular sheet of tin plate 24cm long and 15cm wide is to be formed into a rectangular container open at the top by cutting away a sqaure from each corner and bending up the edges. What is the total area of tin plate to be cut away if the volume of the container is to be a maximum?

i know that you will have formulate the problem to get x (24-2x) (15-2x) and then expand to get 4x^3 -78x^2 + 360x. Then differentiate and simplify. Then find x. I 've tried this and it hasn't come to the right answer.

 

[ksdhart]

Well, your work up to generating the volume seems correct to me, and the process you've outlined is also right. That said, if the answer you're getting is not right, then the error must be in the differentiation and/or simplification. However, without seeing your work on the differentiation, I can't pinpoint where you might have gone wrong. When you reply back, please show all of your steps and what your book/instructor says is the right answer. Thank you.

 

[Robins]

Well, your work up to generating the volume seems correct to me, and the process you've outlined is also right. That said, if the answer you're getting is not right, then the error must be in the differentiation and/or simplification. However, without seeing your work on the differentiation, I can't pinpoint where you might have gone wrong. When you reply back, please show all of your steps and what your book/instructor says is the right answer. Thank you.

Ok I will get back to you, thanks

 

[Robins]

Full workings

Volume= l*w*h

Volume= (24-2x)*(15-2x)*x
F(x) = 4x^3-78x^2+360x
F'(x)= 12x^2-156x+360

Divide by 12

x^2-13x+30

(x-2) (x-15)

x= 2
x= 15

Answer on back of sheet= 36cm^2

 

[stapel]

Volume= l*w*h

Volume= (24-2x)*(15-2x)*x
F(x) = 4x^3-78x^2+360x
F'(x)= 12x^2-156x+360

Divide by 12

Maybe first "set equal to zero"? Because otherwise you've got "F'(x)/12" on the left-hand side.

x^2-13x+30

(x-2) (x-15)

Did you check this?

. . . . .$\displaystyle (x\, -\, 2)(x\, -\, 15)\, =\, x^2\, -\, 2x\, -\, 15x\, +\, 30\, =\, x^2\, -\, 17x\, +\, 30$[/QUOTE]

Did you maybe try the Quadratic Formula? Also, what did you do with the x-values, once you had them? How did you relate them to the actual question? Please show all of your steps. Thank you!