Question

1. A box with a square base and an open top is being constructed from 1200 m² of material. Determine the dimensions of the box that will maximize the volume of the box. Briefly show that your answer gives a maximum. Dimensions (Length x Width x Height):

Answer 1

det a be side of square and y be the height given, Area 1200 m² x+ 1200 1200-72 42 чу ? volume of box fosom egr x2y <?(1307** 300 x- * x3 differentiating witid.no Via 300 22 dll 4 putting . dr dz 20 d7 dxa 300-3x? as x2 = You » 122om also dv 22 / 24. At x = 20 d²v * At x = 20m, volume is maximum from Euro 1200- (20? 10 M Thus the dimension is (Length x width x Height) = 120mx.com xiom ma mx20 Ary