### Abc

Assignment #3

Q 5. Chapter 7
a.

b. Let X11 = amount shipped from Southern Gas to Hamilton County
X12 = amount shipped from Southern Gas to Butler County
X13 = amount shipped from Southern Gas to Clermont County
X21 = amount shipped from Northwest Gas to Hamilton County
X22 = amount shipped from Northwest Gas to Butler County
X23 = amount shipped from Northwest Gas to Clermont County

Min 10X11 + 20X12 + 15X13 + 12X21 + 15X22 + 18X23

s.t. X11 + X12 + X13 <= 500
X21 + X22 + X23 <= 400
X11 + X21 = 400
X12 + X22 = 200
X13 + X23 = 300
X11 + X12 + X13 + X21 + X22 + X23 >= 0

X11 = 0 X21 = 0
X12 = 0 X22 = 0
X13 = 0 X23 = 0

Optimal Solution is 10(0) + 20(200) + 15(300) + 12(400) + 15(0) +18(0) =
4000 + 4500 + 4800 = \$13, 300.

If demand in Butler County is increased by 100 units, the Northwest Gas supplier should be contracted for additional supply.

Q. 7 Chapter 7
a.

b. Let X11 = rate charged by Avery to Client A
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