Minimizing Total Cost of Making Open Box with Squared Base

[jetoso]

Homework Statement

We want to make an open box with squared base. Let x be the dimension of one side of the base and y the height of the box. We pay a cost of $1.00 /cm^2 for the base and $0.50/cm^2 for each side.
The box must have a volume V = 6400 cm^3. Determine the dimensions x and y which will minimize the total cost of making the box.

Homework Equations

V = yx^2, TC = x^2 + 0.5xy

The Attempt at a Solution

I tried to solve the problem taking the partial derivatives with respect to x and y, which will give me the minimum values, but my results are not consistent. I am thinking on using Lagrange multipliers to solve the nonlinear minimization problem subject to the equality constraint of volume.
Any suggestions?
Thank you.

 

[Dick]

In your TC function, remember that the box has four sides. Solve the volume constraint for, say, y. Then substitute that into TC. Now total cost is a function of only x. Minimize it. You certainly don't need lagrange multipliers.

 

[jetoso]

Thank you, I think this works.