An energy company uses three different processes for generating electricity. One of he processes uses wind energy (and so requires no fuel), while the other two consume combination of biofuel and natural gas. Each process also requires some amount of labour and emits some amount of carbon dioxide. The amount of biofuel (in Mg) and natural gas (in mcf = mega cubic feet) consumed, the labour required (in person-hours), the carbon dioxide (CO₂) emitted (in Mg), and the power generated in MWh) per day of operation of each process is as follows: Electricity Process generated 20 32 85 1 2 3 CO₂ Labour produced required 0 20 12 13 29 18 Biofuel required 0 10 30 Natural gas required 0 15 40 Each MWh of electricity can be sold at £144 and there is no limit on the amount hat can be sold. Over its next planning period, the company has 320 person-hours or labour, 75 Mg of biofuel, and 90 mcf of natural gas available. (a) The company emits all the CO2 it produces into the atmosphere. Due to environmental regulations, they cannot emit more than 215Mg of CO₂ in this period. The company wants to know how to operate its processes to generate as much revenue as possible (you may assume that there is no limit on the number of days a process can be run in this period). Give a linear program that models this problem and state what each of your variables represents. You do not need to solve this program. (b) The company decides to make use of a new carbon capture method whereby it can convert some of the CO₂ that it produces into a safe form that is not emitted. Converting 1 Mg of CO2 in this way costs £5. The other resource constraints remain as stated. The company wants to know how to operate its processes to generate as much revenue as possible now also making use of carbon capture (you may assume that there is no limit on the number of days that the processes can operate in this period). Give a linear program that models this problem. You do not need to solve this program.
An energy company uses three different processes for generating electricity. One of he processes uses wind energy (and so requires no fuel), while the other two consume combination of biofuel and natural gas. Each process also requires some amount of labour and emits some amount of carbon dioxide. The amount of biofuel (in Mg) and natural gas (in mcf = mega cubic feet) consumed, the labour required (in person-hours), the carbon dioxide (CO₂) emitted (in Mg), and the power generated in MWh) per day of operation of each process is as follows: Electricity Process generated 20 32 85 1 2 3 CO₂ Labour produced required 0 20 12 13 29 18 Biofuel required 0 10 30 Natural gas required 0 15 40 Each MWh of electricity can be sold at £144 and there is no limit on the amount hat can be sold. Over its next planning period, the company has 320 person-hours or labour, 75 Mg of biofuel, and 90 mcf of natural gas available. (a) The company emits all the CO2 it produces into the atmosphere. Due to environmental regulations, they cannot emit more than 215Mg of CO₂ in this period. The company wants to know how to operate its processes to generate as much revenue as possible (you may assume that there is no limit on the number of days a process can be run in this period). Give a linear program that models this problem and state what each of your variables represents. You do not need to solve this program. (b) The company decides to make use of a new carbon capture method whereby it can convert some of the CO₂ that it produces into a safe form that is not emitted. Converting 1 Mg of CO2 in this way costs £5. The other resource constraints remain as stated. The company wants to know how to operate its processes to generate as much revenue as possible now also making use of carbon capture (you may assume that there is no limit on the number of days that the processes can operate in this period). Give a linear program that models this problem. You do not need to solve this program.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:An energy company uses three different processes for generating electricity. One of
the processes uses wind energy (and so requires no fuel), while the other two consume
a combination of biofuel and natural gas. Each process also requires some amount
of labour and emits some amount of carbon dioxide. The amount of biofuel (in
Mg) and natural gas (in mcf = mega cubic feet) consumed, the labour required (in
person-hours), the carbon dioxide (CO₂) emitted (in Mg), and the power generated
(in MWh) per day of operation of each process is as follows:
Process
1
2
3
Electricity
generated
20
32
85
CO₂
produced
0
12
29
Labour Biofuel
required
required
20
0
13
10
18
30
Natural gas
required
0
15
40
Each MWh of electricity can be sold at £144 and there is no limit on the amount
that can be sold. Over its next planning period, the company has 320 person-hours
for labour, 75 Mg of biofuel, and 90 mcf of natural gas available.
(a) The company emits all the CO₂ it produces into the atmosphere. Due to
environmental regulations, they cannot emit more than 215Mg of CO₂ in this
period. The company wants to know how to operate its processes to generate
as much revenue as possible (you may assume that there is no limit on the
number of days a process can be run in this period). Give a linear program
that models this problem and state what each of your variables represents. You
do not need to solve this program.
(b) The company decides to make use of a new carbon capture method whereby
it can convert some of the CO₂ that it produces into a safe form that is not
emitted. Converting 1 Mg of CO2 in this way costs £5. The other resource
constraints remain as stated. The company wants to know how to operate
its processes to generate as much revenue as possible now also making use of
carbon capture (you may assume that there is no limit on the number of days
that the processes can operate in this period). Give a linear program that
models this problem. You do not need to solve this program.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 7 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
