Question 203505
"length (l) of the base is three times the width (w)" ___ L = 3W


"2250 cubic inches of volume" ___ V = L * W * H ___ 2250 = 3W * W * H ___ 750 / W^2 = H


surface area = (L * W) + 2 (L * H) + 2 (W * H) = 3W^2 + 4500/W + 1500/W = 3W^2 + 6000/W
___ you need to find the minimum of this function


finding the slope of the curve (first derivative) and setting equal to zero -- this is the minimum
___ 0 = 6W - 6000/(W^2) ___ 6000/(W^2) = 6W ___ 1000 = W^3 ___ 10 = W


substituting ___ L = 3(10) = 30 _____ H = 750 / (10^2) = 7.5