A rectangular box (dimensions x, y and z) is to be constructed with material that costs 1€ per square cm for the bottom, 2€ per square cm for the sides, and 5€ per square cm for the top. If the total volume is to be 96 cm³, what is the minimum cost for constructing this box?

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ISBN:9780470458365
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4141 Constrained optimization. Please solve without AI and clear handwriting. Thank you

A rectangular box (dimensions x, y and z) is to be constructed with material that costs 1€ per square cm
for the bottom, 2€ per square cm for the sides, and 5€ per square cm for the top. If the total volume is
to be 96 cm³, what is the minimum cost for constructing this box?
Transcribed Image Text:A rectangular box (dimensions x, y and z) is to be constructed with material that costs 1€ per square cm for the bottom, 2€ per square cm for the sides, and 5€ per square cm for the top. If the total volume is to be 96 cm³, what is the minimum cost for constructing this box?
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