A retrofit HVAC project includes installing rectangular air ducts in braced floor joists. The dimensions of the joist and floor joist are shown in Figure P6.18. The duct is to be designed such that the pressure drop through the duct is minimized.

This occurs when the duct has the maximum cross-sectional area.

a. Write the formal optimization statement in the form of Equation set 6.26.

b. Solve the optimization problem by combining the constraint with the objective function and solving the resulting unconstrained problem.

c. Solve the optimization problem using the method of Lagrange multipliers.

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FIGURE P6.18 Air duct in a retrofit HVAC project. h 32 in W 24 in