(Solved): (1 point) Design a rectangular milk carton box of width \( w \), length \( l \), and height \( h \) ...

(1 point) Design a rectangular milk carton box of width \( w \), length \( l \), and height \( h \) which holds \( 458 \mathrm{~cm}^{3} \) of milk. The sides of the box cost \( 2 \mathrm{cent} / \mathrm{cm}^{2} \) and the top and bottom \( \operatorname{cost} 4 \mathrm{cent} / \mathrm{cm}^{2} \). Find the dimensions of the box that minimize the total cost of materials used. dimensions = (Enter your answer as a comma separated list of lengtns.)