Question

PaGas is an energy corporation based in Pennsylvania. Currently, it has one fracking
site, two gas extraction plants and a water recycling plant. The fracking site fractures the ground by
pumping water, it requires 50 barrels (bbl) of water per day. The gas extraction plants generate water
waste which cannot be disposed on the ground. This water must be either transported to the fracking
site or to the water recycling plant. Currently, gas extraction plant A is generating 20 bbl/day of water
waste while gas extraction plant B is generating 25 bbl/day. If the total amount of water transported
to the fracking site is not enough to meet the daily demand of 50 bbl, then the company must purchase
freshwater at a cost of $70 per bbl in order to do so.
You are helping the manager of PaGas run their daily water operation. This involves deciding where to
transport the water generated from each gas extraction plant (either to the fracking site or to the water
recycling plant), and how much freshwater to purchase at the fracking site. The cost of transporting
1 bbl of water from the gas extraction plants A and B, to the fracking site and the water recycling
plants can be found in the following table:
From Gas
Extraction
Plant

To Fracking Site To Water
Recycling Plant
A $200 $100
B $180 $120

Use the following decision variables:
• XAF : Daily amount of water transported from gas extraction plant A to the fracking site.
• XBF : Daily amount of water transported from gas extraction plant B to the fracking site.
• XAR: Daily amount of water transported from gas extraction plant A to the water recycling plant.
• XBR: Daily amount of water transported from gas extraction plant B to the water recycling plant.
• XF : Daily amount of freshwater purchased at the fracking site.
Answer the following questions:
(a) (5 points) What is the total daily cost of running the water operation? (state it as a function
of the five decision variables). This involves the water transportation costs and the freshwater
purchase cost.

1

(b) (4 points) State the constraints for gas extraction plants A and B. All the water they produce in
a day must be transported to another location. (Here you will state two constraints, one for plant
A and another one for plant B)

(c) (4 points) State the demand constraint for the fracking plant. The total water transported to it
in addition to the freshwater bought must meet its demand.

(d) (7 points) State a linear program (LP) that minimizes the cost of running the water operation for
PaGas. You do not need to solve this LP, but make sure it has all required constraints.

Answer 1