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

X12 = rate charged by Avery to Client B

X13 = rate charged by Avery to Client C

X14 = rate charged by Avery to Client D

X21 = rate charged by Baker to Client A

X22 = rate charged by Baker to Client B

X23 = rate charged by Baker to Client C

X24 = rate charged by Baker to Client D

X31 = rate charged by Campbell to Client A

X32 = rate charged by Campbell to Client B

X33 = rate charged by Campbell to Client C

X34 = rate charged by Campbell to Client D

Max 100X11 + 125X12 + 115X13 + 100X14 + 120X21 + 135X22 + 115X23 + 120X24 +

+ 155X31 + 150X32 + 140X33 + 130X34

s.t. X11 + X12 + X13 + X14 <= 160

X21 + X22 + X23 + X24 <= 160

X31 + X32 + X33 + X34 <= 140

X11 + X21 X31 = 180

X12 + X22 X32 = 75

X13