The top and bottom margins of a poster are 4 cm and the side margins are each 8 cm. if the area of printed material on the poster is fixed at 388 square centimeters, find the dimensions of the poster with the smallest area.

Illustrate the given problem. Refer to the diagram attached to aid our solution.

Area of bigger rectangle:
A = (L+8)(W+16)

Area of smaller rectangle (printed area)
388 = LW

From the second equation, we can express L in terms of W.
L = 388/W
Replace this to the first equation:
A = (388/W+8)(W+16)
A = 388 + 6208/W + 8W + 128
A = 6208/W + 8W + 516
Derive A with respect to W and equate to zero (calculus):
dA/dW = -6208/W² + 8 = 0
-6208/W² = -8
W² = -6208/-8 = 776
W = √776 = 27.86 cm
L = 388/27.86 = 13.93 cm

Thus, the smallest area would be:
A = (13.93 cm)(27.86 cm)
A = 388.09 cm²

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