Optimization Fish Tank

J

joey123

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Oct 23, 2005
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A glass fish tank is to be constructed to hold 72 cubic feet of water. It's base and sides are to be rectangular, and the top is open. It is to be constructed so that its width will be 5 feet but the length and depth are variable. Building the tank costs 10 dollars per square foot for the base and 5 dolalrs per square foot for the sides. What is the cost of the least expensive tank?
 
Where are you having difficulty? You've picked variables for the length and the depth, formed the volume equation (using the given values for volume V and width w), and solved for one of the variables. And... then what?

Please reply showing what you have tried. Please be specific. Thank you.

Eliz.
 
So start working with the surface-area information. You know how to find areas of rectangles, right?

If you get stuck, please reply showing your work. Thank you.

Eliz.
 
how do you factor in anew equation for the cost per square foot of the tank and substitute a variable found in the volume equation into it?
 
If you're asking this question, then I have to think you haven't done the steps I'd suggested earlier, since the result would have answered this question.

Please reply showing your work. Thank you.

Eliz.
 
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