$1\mathrm{.}17.$ A waste heat boiler $($see Fig. P$1\mathrm{.}17)$ is to be designed for steady state operation

under the following specifications.

Total gas flow:

Gas composition:

Gas temperatures:

Stream pressure outside tubes:

Gas properties:

Cost data are:

Base the optimization on just the cost of the shell, tubes, and pumping costs for the

gas. Ignore maintenance and repairs.

$25,000k\frac{g}{h}$

$S{O}_2(9\%),O_2(12\%),N_2(79\%)$

$in=1200C$; out $=350C$

$250$kPa

$C_p=0\mathrm{.}24$kca$\frac{l}{g}(C)$

$=0\mathrm{.}14k\frac{g}{m}(h)$

$k=0\mathrm{.}053$kca$\frac{l}{m}(h)(C)$Formulate the optimization problem using only the following notation $($as

needed$)$:

How many degrees of freedom are in the problem you have formulated?