Expert: Paul Klarreich - 11/15/2008

Question
QUESTION: I have a problem that needs to maximize a half cylinder shaped airplane hangar to 225,000 sqft. I am having a difficulty determining how to minimize the cost of the building. Also, I need to find the total dimensions of the building.

The costs for the buildings pieces are:
$30 per square foot for the foundation,
$20 per square foot for the two ends, and
$15 per square foot for the roofing.

C(t)= (2ry30)+(piry15)+(pir^2*20)
C(t)= Total cost model
V=1/2pir^2y=225000


ANSWER: Hi, Tony,

We did this already.  See:

http://en.allexperts.com/q/Calculus-2063/2008/10/Maximum-minimum-problems-11.htm

if you get stuck, send me what you did and I'll try to help.



---------- FOLLOW-UP ----------

QUESTION: I am having a difficult time understanding how to minimize the cost of the building and finding the actual dimensions of it. I looked at the the problem you initially did and I understood how to get the equations, but not past that. sorry, and thank you for any help you can give.

Tony

Answer
Questioner:   Tony Salatti
Category:  Calculus
Private:  No
 
Subject:  Maximum-Minimum problem
Question:  QUESTION: I have a problem that needs to maximize a half cylinder shaped airplane hangar to 225,000 sqft. I am having a difficulty determining how to minimize the cost of the building. Also, I need to find the total dimensions of the building.

The costs for the buildings pieces are:
$30 per square foot for the foundation,
$20 per square foot for the two ends, and
$15 per square foot for the roofing.

C(t)= (2ry30)+(piry15)+(pir^2*20)
C(t)= Total cost model
V=1/2pir^2y=225000


ANSWER: Hi, Tony,

We did this already.  See:

http://en.allexperts.com/q/Calculus-2063/2008/10/Maximum-minimum-problems-11.htm

if you get stuck, send me what you did and I'll try to help.



---------- FOLLOW-UP ----------

QUESTION: I am having a difficult time understanding how to minimize the cost of the building and finding the actual dimensions of it. I looked at the the problem you initially did and I understood how to get the equations,

>> THAT was the hard part.  


but not past that. sorry, and thank you for any help you can give.

Tony

........................................


If this is your first time doing a Maximum-minimum problem, here is the scheme.

1. Identify the variables in the problem -- the things that change.  Give them names.

2. Find the one that is to be 'optimized'.  Write it as a function of the other variables.

3. If it is a function of more than one, use the other conditions (constraints) to eliminate all but one.

4. Differentiate, set that = 0, solve for your 'stationary' point.

5. Consider whether it is a maximum, minimum, or neither.  Check the logical endpoints, too.

6. Answer whatever other questions are asked.

........................
Now just what part of it are you stuck on?  The derivative is routine -- a polynomial with some negative exponents.  Then you will have some calculao work.

Send me what you were able to do.  Except for slightly different numbers, this was the problem you had.

If you don't know what steps 4,5,6 mean, that is really your teacher's responsibility.