An open-topped box is to be constructed with a base whose length is twice its width. The material for the sides is three times as expensive as the base. If the volume of the box is to be 6 m, determine the dimensions of the box that minimizes the cost of construction. #6. C- (212 + 3(6xy)- 2x² +19xy 18x() = 21? + 54 %3D C(x)= 212 + 2x ズ 21 c'1x) = 41- 54 =0 =7 4x3=54 V = 22?y=6 6. x3 3 E 2.39 m 2 i min. cost of construction when c'ci) =-50 --50 2.38 c'(4)=2.5 3. 2 0.52 m the dimensrons are 4.76x 2.38 x 0.52 m 26 2.3

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