The base of a rectangular aquarium with given Volume V is made of slate and the

Question

The base of a rectangular aquarium with given Volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass find the dimensions x, y, z of the aquarium that minimize the cost of the materials.

(Hint: 1. That the volume has the constant value V gives you the constraint equation; that means your answers for the dimensions will be in terms of the constant V, i.e expressions in terms of V.

2. Since only the ratio between the costs of the two materials seems to matter, you may as well make it a little more concrete by assuming slate costs $5 per unit area and glass costs $1 per unit area)

Explanation / Answer

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