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.