Hello, leinadwerdna!

Did you make a sketch?

Lagrangeco, inc. has to build a rectangular steel box with an open top of volume 96 cm³.

The bottom of the box costs three times as much per cm² as the four sides.

What dimensions of the box will minimize the cost? Code:

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L

The cost of the steel is dollar/cm² for the sides

. . and dollars/cm² for the bottom.

The bottom has cm² of steel at dollars/cm².

. . Its cost is: . dollars.

The four sides has cm² of steel at dollars/cm².

. . Their cost is: . dollars.

The total cost is: . dollars.

Got it?