Hello, khuezy!

Concrete costs $15/m², and glass costs $100/m².

If the volume of the pool must be 1000 m³,

what should the dimensions be to minimize the cost of the pool?

One of the sides is glass; the bottom and other 3 sides are concrete.

.[1]

Surface area: . This is all correct, but you forgot about the *Cost*. Code:

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z| G | /y
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Suppose the front face is glass.

Its area is m² and costs $100/m².

. . Its cost is: . dollars.

The rest of the area is: . m² at $15/m².

. . Its cost is: . dollars.

The total cost is: .

Substitute [1]: .

. . and we have: .

Set the partial derivatives equal to zero . . .

. .

Multiply [2] by .[4]

Multiply [3] by .[5]

Substitute [4] into [5]: .

. .

Substitute into [4]: .

Substitute into [1]: .