Another Optimization Problem Help

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Ghost3k

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A large bin for holding heavy material must be in the shape of a box with an open top and a square base. The base will cost 7 dollars a square foot and the sides will cost 9 dollars a foot. If the volume must be 180 cubic feet. Find the dimensions that will minimize the cost of the box's construction.

Base :
Each side :

I have an idea of what it should look like but I have no idea how to create the equations for this. Can someone enlighten me. I just really need to know the basic equations. But the entire process would be great. Thanks
 
Base Area = S*S -- The Base is square.

H = Height of box

Box Volume = H*S*S = 180 ft^3

Now what?

Note: The most important thing we see, here, is WRITING definitions of things.
 
tkhunny said:
Base Area = S*S -- The Base is square.

H = Height of box

Box Volume = H*S*S = 180 ft^3

Now what?

Note: The most important thing we see, here, is WRITING definitions of things.
Click to expand...

Im not sure, where does the 7 dollar and 9 dollar come into place. Yes you are right, the most important part about these problems is writing the definitions. would S^2 = 7 and H be 9? Help me out please, I'm trying to understand it but I just dont see what I'm supposed to do. I know that you usually take the derivative and set it equal to zero and solve, but I don't know how to set up the equation to take the derivative of.
 
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JeffM said:
First IDENTIFY ALL the variables relevant to the problem and LABEL THEM. This is the first step in solving any word problem.

H = height of box.
W = width of square base.
B = area of base.
W = area of walls.
V = volume of box.
C = cost of box. tkhunny was not going to do all the work for you. I won't either in the future.

Second, USING YOUR LABELS, state the problem to be solved and identify a method to do so.

Minimize C subject to constraint that V = 180. What technique is used to solve optimization problems subject to a constraint?

Third, USING YOUR LABELS, write down any general information relevant to your variables or information given in the problem. In particular what is C and what is V. V is easy.

V = W * B2.

What is C (here is where your 7 and 9 come in)?

Fourth, you no longer have a word problem. Everything from this point on is mechanics. Solve and relax. Clue you will be looking for partials in three variables.
Click to expand...

Thanks for your reply, I got the answer now.
 
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