Question 1720
 Let the height ofthe U shape be h inches and the width be w inches.
 Since 2h+ w = 14, so w = 14 -2h.

 The volume V of the U shape is V(h) = 8 hw = 8 h(14 -2h) = 16 h(7-h).
 
 Since,0 < 2h < 14, the domain of the function V(h) is (0,7).
 Note that V(h) = 16 h(7-h) = -16[h^2-7h+ (7/2)^2] + 49*4
                = -16(h- 7/2)^2 + 196 <= 196
 Clearly, V(h)>0, so the range of the function V is (0, 196].  

 since -16(h- 7/2)^2 <=0, we see that when h = 7/2 (inches),
 the volume has max value 196 cubic inches.



 Kenny