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

Introducing these restrictions in (38), and simplifying, gives:
(6) P- (C 2 - C 2 )Y-CX-L =P • - (6 2 - C 2 ) 2 Y-CX+CX- L
a t wa 0 wa 0 wa b t wb 0 wb 3 wb 0
or
+C)X+L - L
b a wb 3 wb wa 0 wa wb
(7) . Y -
0
i
i 15.
subject to X 2
Subject to
E , c2 _ c2 .1 _ (02 _ 02 1 1
. 1" ‘ t wb' ‘ t wa' J
The boundary is linear. At Y o = 0,
•
P a -P b +C wb X 3 -L wa +L
'0_ C wb + C wa
For the competition between water transportation to a and rail
transportation to A, the indifference locus is defined by
1 1
2
(8) . Pa - Cr (X 2 0 + Y 2
0 ) 2 - Lr = Pb - Ct [(X2 - X0 ) 2 + Y1 o - Lt - LwB - CwB (X 3 - X 2 )
and X X > 0.
0' 2 '
,Simplifying and transforming (4) 1 as was done previously, it can
be seen easily that the branches of the boundary are segments of hyperbolas.
At Y = 0
0 '
X =P-P+CX+L+L -L it
0 a b wb 3 t wb r Cwb + C r . •
Similarly, for the competition between water transportation to . 8 and truck
transportation to A, the indifference locus is given . be
1
2
+ Y2
0 ) 2 - L = P - C [(X
2 21
. - X ) + Y j - L - L -
a
t t b t 2 0 o t wL
(9) P - d (x 2 0
siblY01
1
83
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