I went over the question again on lunch break, I realized I made some errors.

Solve for h:

v=lxwxh

1440cm3=2x(x)+h

h=1440cm3/(2x^2 )

find the cost.

c=Lid+Base+Long sides+Short sides

c=4c(2x^2 )+c(2x^2 )+c 1440/(2x(2x^2))+c 1440/(x(2x^2))

Find the derivative:

c^'=16cx+4cx+c(-1)(1440)(2x) (2x^2 )^(-2)+c(-1)(1440)(x) (2x^2 )^(-2)

Let c' = 0 and solve for x.

0=16cx+4cx+c(-1)(1440)(2x) (2x^2 )^(-2)+c(-1)(1440)(x) (2x^2 )^(-2)

I ended up with:

x=5sqrt6460

x= 401.87

I don't feel like that's right. Once I get the value for x I should be good to solve for the dimensions.