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let the dimensions of base = x ft let the height be h cm volume, V = x^2 h = 20 h = 20 / x^2 area of base = x^2 area of top = x^2 area of 4 sides = 4xh Total Cost, C = 0.3x^2 + 0.2 x^2 + 0.1(4xh) C = 0.5x^2 + 0.4 xh substitute h = 20 /x^2 C = 0.5 x^2 + 8 / x differentiating dC/dx = x - 8 x^2 inorder to minimize cost , equate dC/dx to 0 x - 8/x^2 = 0 x^3 = 8 x = 2 ft h = 20 /4 = 5 so dimensions of box are 2 x 2 x 5 ft

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