Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

Until now, no attention has been paid to the loading and unloading
costs. Introducing them in the analysis gives the next equation:
(6) CZ ta + L t = CZb t + L t + CZ w ab +L w
where.I. t and L w are the costs of loading and unloading a ton of grain,
transported by truck and by water respectively. Equation (6) becomes:
(7) Za - Zb = Cw /Ct • Zab + Lw /Ct
w = 0, equation (7) becomes:
Za - Zb = Lw/Ct ,
and in place of a straight line through the mid-point, the boundary will be
a hyperbola with vertex at the right of the mid-point, since Lw is a constant.
In this case, the distance between the mid-point and the vertex is equal to .
L /2C When C
w
is not equal to zero, this distance L /2C must be added to
t' w w t
C /2C • Z to obtain the total distance from the vertex to the mid-point.
w t ab'
This is illustrated in Diagram 3. The major result of introducing the
handling cost in the model, is to reduce the number of farmers who use the
waterway.
Thus, if C
It was assumed that every point in the space was in straight-line
connection with every other by means of road and at the same time, that road
and water were the only transportation means available. In order to make
model more realistic, we assume now that, while every point in space is still
in straight-line connection with B by truck, the farmers can reach A by rail
only. This modification hardly brings more realism into the model, but is
useful as an expository device.
For the time being this provides us with a new equattion:
(6) CZ +L =CtZb +L
ra r t tap + L w
where C r, and L r respectively are the constant rate per ton-mile of grain by
rail and the loading-unloading cost by rail. We may define C t kCr , and
rewrite (8) as
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