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1. The problem statement, all variables and given/known data

Find the most economical dimensions of a closed rectangular box of volume 8 cubic units if the cost of the material per square unit for (i) the top and bottom is 5, (ii) the front and back is 2 and (iii) the other two sides is 5.

(a) What is the length of the vertical edge?

(b) What is the length of the horizontal front and back edge?

(c) What is the length of the horizontal side edge?

2. Relevant equations

Lagrange Multiplier Method or equivalent.

3. The attempt at a solution

The Lagrange Multiplier method is not required for this problem so if there is an easier way please notify me of it as well as why it's easier. My work is attached but I'm stuck at the step of figuring out the variables/dimensions.

Any help would be GREATLY appreciated!

Thanks in advance!

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# Homework Help: Find the most economical dimensions of a closed rectangular box [. . .]

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