Question

A shipping company must design a closed rectangular shipping crate with a square base. The volume is 8748 ft". The material for the top and sides costs $3 per square foot and the material for the bottom costs $6 per square foot. Find the dimensions of the crate that will minimize the total cost of material. Answer 7 Points Keypad Keyboard Shortcuts ft by ft by ft

Answer 1

Volume 28148 (pt) cast for Material for top & sides - 3 per sq.ft Material for baklom 6 per sqft Let the dimension of the create are x,x,h Volume Area upper base x2 cast for upper base = 3 x² Area of lower baso - xe² cast for lower base = bac2 Area of sick walls - och Area of all 4 side walls hoch cast of all 4 side walls 3x hoch 12 och 22h Total cast = T = 3x² + 6x2 + 12xch az + 12 och Also volume x² =8748 h=8748 Test T = 9x2 + 12x (8748 9x² + 104976

Min cast, T'(x) = 0 T'(d) + 781 = 104976 2 18x = 104976 x = 5832 02 x = 18 ft n = 2 8748 = 27 ft x² Dimensions of the crate are 18 ft by 18 ft by 27 pt
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