# Making a box

1. Dec 4, 2007

### jetoso

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
V = yx^2, TC = x^2 + 0.5xy

3. 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.

2. Dec 4, 2007

### 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.

3. Dec 4, 2007

### jetoso

Thank you, I think this works.