A rectangular duct mounted beneath the beams in

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A rectangular duct mounted beneath the beams in a building, as shown in Figure 3, is to have a cross-sectional area of 0.9 m2. The cost of the duct for the required length is $200 per meter of perimeter. The building must be heightened by the amount of the height of the duct, and that cost is $1.00 per millimeter. After the duct has been sized to provide minimum total cost, the possibility of enlarging the duct is explored. What is the additional cost per square meter of cross-sectional area of a very small increase in the area?

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