It is obvious that for a system with only one size pipe a given insulation thickness t is associated with a unique value of Q and a corresponding cost C. Thus, one can wrap a pipe with a required amount of insulation to achieve an acceptable heat loss Q by paying a dollar cost C. Q and C are calculated by (A-19) and (A-20) for n = 1. But when two or more pipe diameters are in the network then there is a variety of ways that the insulation thickness can be designed to produce a specified heat loss, i.e., a small diameter pipe may receive a very thick insulation combined with a larger pipe receiving a small thickness, or vice versa. Either way the system heat loss could be the same. But for a specified system heat loss Q it is apparent that the insulation thickness application strategy which is optimal is that which will minimize the cost. Thus, with the as the sole variable (all other parameters are fixed) the cost as figured by equation (A-20) must be minimized subject to the
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