A retrofit HVAC project includes installing rectangular air ducts in braced floor joists. The…

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.