optimization problem

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Solve the perimeter equation for r or h and sub into the area formula.

Solve the perimeter for h, then sub into area we get:

\(\displaystyle A=\frac{3200r-r^{2}(\pi +4)}{2}=1600r-\frac{r^{2}}{2}(\pi +4)\)

Can you differentiate this?.

Then, set the derivative to 0 and solve for r. h follows by re-subbing back into the perimeter formula solved for h.
 
Last edited:
pastaa said:
I know that the total perimeter is 2h + 2r + πr = 1600, where π is pi ◄◄ This line is correct.



therefore, h=(1600-2h-2r)/2 ◄◄ This line is not correct.

You may not express h in terms of itself. Please try solving again the perimeter equation for h.



The total area then is equal to A = (πr2)/2 + (1600-2h-2r)/2 ◄◄ This line is not correct.

(Pi r^2)/2 is certainly the area of the semi-circular part, but why did you use the expression for what you thought was height for the area of the rectangular part?

The area of a rectangle is the product of its dimensions. The dimensions of the rectangular part are h and 2r.
Click to expand...

galactus already explained how he determined his function for total area in terms of r.

(1) Solve the perimeter equation for h

(2) Substitute the result for symbol h in the area formula.


You need to first fix your solution for h and fix your area formula; then try galactus' method for obtaining the total area function in terms of r.
 
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