TM 5-813-8
Step 9: Analyze the Minimum Corner and Edge Constraints Solutions from Step 6 with respect to the assumptions and
scenarios in Step 8.
a. Since Cx > Cy and for the minimum cost solution to be all double-pass water such as Case a, Step 6, Cx > Cy,
blending should be done for economy.
b. When water x and y are the only components of a blend Case B, Step 6 shows
Cx < 0.0427 Cy + .957 Cz
and Step 8, Case g shows
.85 Cx > Cy > Cz
Therefore, 1.176 Cy 0.0427 Cy + .957 Cz
or 1.134 Cy < Cz,
which violates the second half of Step 8, Case g, unless the cost of well water really is greater than 1.13 times the
cost of first-stage reverse osmosis sea water desalination.
c. When water x and z are the only components of a blend
Case C, Step 6 shows
Cx < 1.066 Cy - 0.066 Cz
and Step 8, Case b shows
Cx > 1.176 Cy
Therefore, 1.176 Cy < 1.066 Cy - 0.066 Cz
or 0.11 Cy < - 0.066z,
so this cannot be an optimum solution unless someone is paying you to dispose of well water z.
d. When 6.5 gallons/minute of first-stage reverse osmosis product water is used in a triple blend Step 6, Case d
shows
16.25 Cy - 15.25 Cx < Cz < 0.1615 Cx
+ 0.838 Cy
and Step 8, Case f shows
.5 Cx < Cy > Cz usually
Therefore,
16.25 Cy - 15.25(2 Cy) < Cz < 0.1615(2Cy)
+ 0.838 Cy
or - 14.25 Cy < Cz < 1.161 Cy,
so for any cost from being paid 14.25 times the cost of water y to dispose of well water z to having water z cost
1.161 times water y the optimum cost solution will be this triple blend.
e. When the acceptable triple blend of
224 gallons/minute of water x
224.5 gallons/minute of water y
and 51.5 gallons/minute of water z
is most economical, Step 6, Case e shows
0.1615 Cx + 0.838 Cy < Cz < 1.0447 Cx
- 0.0447 Cy
and Step 8, Case f, shows
.5 Cx < Cy > Cz usually
and Step 8, Case g shows
.85 Cx > Cy > Cz usually
Therefore,
(0.1615)(1.176 Cy) + 0.838 Cy < Cz 1.0447 (2 Cy)
- 0.0447 Cy
1.0279 Cy < Cz < 2.0447 Cy
so this blend will be economical only if the cost of well water is greater than the cost of single-pass desalinated sea
water by more than 1.03 times and less than 2.04 times as expensive as single-pass desalinated sea water. These
conditions violate the second part of Step 8, Cases f and g.
Step 10: Draw Conclusions
a. The most economical blending strategy on the island will almost certainly be: 182 gallons/minute of high quality
second-stage, product-staged reverse osmosis desalinated sea water
A-39
Previous Page
