PaGas is an energy corporation based in Pennsylvania. Currently, it has one fracking site, two gas…

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.