I am totally lost with this problem.
The length of a cedar chest is twice its width. The cost/dcm^2 of the lid is four times the cost/dcm^2 of the rest of the cedar chest. If the volume of the cedar chest is 1440 dcm^3, find the dimensions so that the cost is a minimum.
They are typos. I was very tired when I made the original post. I should have wrote "dcm" in both cases. Even on the diagram I have labelled the cedar chest to have a a volume in cubic centimeters where it should be decimeters. 1440dcm cubed
One cubic decimeter is: 10cm * 10cm * 10cm
** Of course I have edited it now.
C = the total cost for producing the cedar chest.
V = 1440 - In someway I have to take this value and substitute it into the equation so I can determine the value of at least 1 variable.
Then, I have to find the derivative, and solve for x when it is equal to zero.
I am not sure how I can go about expressing the total cost with only a single variable.
Obviously, what you posted was not a pristine solution. Nonetheless, why have you expressed the volume as 2x^2h? That makes absolutely no sense to me. I do not see how that is algebraically equivalent to expressing V as 2x^2 * h. However, it must mean something to you. If you would care to explain...
Thanks in advance.
Could you please show me where I went wrong.
Thanks in advance!
...sorry don't know large bracket command
Solve for x when the derivative is equal to zero.
Dimensions obtained: W= 9.44 L=18.88 h=16.16
These don't work out to equal 1440, So I know I am going wrong somewhere. Can't seem to pinpoint exactly where.
Once again, thanks a lot for your help.