Your professor's advice is correct . . .
A carpenter has been asked to build an open box with a square base.
The sides of the box will cost $3/mē, and the base will cost $4/mē.
What are the dimensions of the box of greatest volume
that can be constructed for $48?
The answer is supposed to be: 2 by 2 by 4/3 meters
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The base has an area of mē.
. . At $4/mē, its cost is: . dollars.
The four sides have an area of mē.
. . At $3/mē, their cost is: . dollars.
The total cost is: . which is limited to $48.
. . There is our constraint: . .
The volume of the box is: . .
Substitute  into : .
. . And we have: .
And that is the function we must maximize . . .