Call Now to Set Up Tutoring:

(888) 888-0446

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

All Math Modeling Resources

20 Practice Tests Question of the Day Flashcards Learn by Concept

Want to review Math Modeling but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different Math Modeling flashcards! Our Math Modeling flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous Math Modeling flashcards.

Flashcards: Linear Programming

A farm has 750 acres of land available for planting crops. The possible crops are soy, corn, and oats. There is 1,200 acre-ft of water for irrigation and the crew will be able to work of the farm 575 hours per week.

Find the amount of each crop that should be planted to maximize the profit.

The table below includes some additional, helpful information.

$\begin{tabular}{|c|c|c|c|} \hline requirements (per acre) &soy &corn& oats\\ \hline Irrigation&2.2&1.1&1.2\\ Labor & 0.9&0.1&0.2\\ Money Made&400&250&300 \\ \hline\end{tabular}$

$\\x_1=510 \\x_2=0 \\x_3=65\\y=\$223,500$

$\\x_1=150 \\x_2=70 \\x_3=65\\y=\$243,500$

$\\x_1=65 \\x_2=0 \\x_3=510\\y=\$223,500$

$\\x_1=210 \\x_2=100 \\x_3=65\\y=\$253,300$

$\\x_1=500 \\x_2=65 \\x_3=15\\y=\$233,500$

Report an Error Copyright Notice

Flashcards: Linear Programming

Find the amount of each crop that should be planted to maximize the profit.

The table below includes some additional, helpful information.

$\begin{tabular}{|c|c|c|c|} \hline requirements (per acre) &soy &corn& oats\\ \hline Irrigation&2.2&1.1&1.2\\ Labor & 0.9&0.1&0.2\\ Money Made&400&250&300 \\ \hline\end{tabular}$

Your answer:

$\\x_1=150 \\x_2=70 \\x_3=65\\y=\$243,500$

Your answer:

$\\x_1=65 \\x_2=0 \\x_3=510\\y=\$223,500$

Your answer:

$\\x_1=210 \\x_2=100 \\x_3=65\\y=\$253,300$

Your answer:

$\\x_1=500 \\x_2=65 \\x_3=15\\y=\$233,500$

Correct answer:

$\\x_1=510 \\x_2=0 \\x_3=65\\y=\$223,500$

Explanation:

The objective of this particular problem is to maximize the profit.

Maximize the function:

y=f(x_1,...,x_n)=c_1x_1+...+c_nx_n

over the region defined by the constraints.

First identify the variables and assumptions of the problem.

$\\x_1=\text{acres of soy planted} \\x_2=\text{acres of corn planted} \\x_3=\text{acres of oats planted} \\l=\text{labor required} \\w=\text{water required} \\t=\text{total acreage planted} \\y=\text{total profit}$

$\\w=2.2x_1+1.1x_2+1.2x_3 \\l=0.9x_1+0.1x_2+0.2x_3 \\t=x_1+x_2+x_3 \\y=400x_1+250x_2+300x_3 \\w\leq 1200 \\l\leq 750 \\t\leq 575 \\x_1\geq0, x_2\geq0, x_3\geq 0$

Now using the constraints formulate the linear programming model.

$\\2.2x_1+1.1x_2+1.2x_3\leq1200 \\0.9x_1+0.1x_2+0.2x_3\leq750 \\x_1+x_2+x_3\leq575 \\x_1\geq0, x_2\geq0, x_3\geq 0$

From here use computer implementation to solve using the simplex method.

$\\x_1=510 \\x_2=0 \\x_3=65$

Therefore, the optimal solution will occur when there are 510 acres of soy planted and 65 acres of oats.

The maximum profit at this solution will be, $223,500.

Flashcards: Linear Programming

Find the amount of each crop that should be planted to maximize the profit.

The table below includes some additional, helpful information.

$\begin{tabular}{|c|c|c|c|} \hline requirements (per acre) &soy &corn& oats\\ \hline Irrigation&1.2&3.4&1.9\\ Labor & 0.1&0.8&0.3\\ Money Made&300&550&200 \\ \hline\end{tabular}$

$\\x_1=343.182 \\x_2=0 \\x_3= 231.818\\y=\$230,454.50$

$\\x_1=0 \\x_2=231.818 \\x_3=343.182\\y=\$230,454.50$

$\\x_1=343.182 \\x_2=231.818 \\x_3=0\\y=\$230,454.50$

$\\x_1=231.818 \\x_2= 343.182 \\x_3=0\\y=\$230,454.50$

$\\x_1=231.818 \\x_2=0 \\x_3=343.182\\y=\$230,454.50$

Report an Error Copyright Notice

Flashcards: Linear Programming

Find the amount of each crop that should be planted to maximize the profit.

The table below includes some additional, helpful information.

$\begin{tabular}{|c|c|c|c|} \hline requirements (per acre) &soy &corn& oats\\ \hline Irrigation&1.2&3.4&1.9\\ Labor & 0.1&0.8&0.3\\ Money Made&300&550&200 \\ \hline\end{tabular}$

Your answer:

$\\x_1=343.182 \\x_2=0 \\x_3= 231.818\\y=\$230,454.50$

Your answer:

$\\x_1=0 \\x_2=231.818 \\x_3=343.182\\y=\$230,454.50$

Your answer:

$\\x_1=231.818 \\x_2= 343.182 \\x_3=0\\y=\$230,454.50$

Your answer:

$\\x_1=231.818 \\x_2=0 \\x_3=343.182\\y=\$230,454.50$

Correct answer:

$\\x_1=343.182 \\x_2=231.818 \\x_3=0\\y=\$230,454.50$

Explanation:

The objective of this particular problem is to maximize the profit.

Maximize the function:

y=f(x_1,...,x_n)=c_1x_1+...+c_nx_n

over the region defined by the constraints.

First identify the variables and assumptions of the problem.

$\\w=1.2x_1+3.4x_2+1.9x_3 \\l=0.1x_1+0.8x_2+0.3x_3 \\t=x_1+x_2+x_3 \\y=300x_1+550x_2+200x_3 \\w\leq 1200 \\l\leq 750 \\t\leq 575 \\x_1\geq0, x_2\geq0, x_3\geq 0$

Now using the constraints formulate the linear programming model.

$\\1.2x_1+3.4x_2+1.9x_3\leq1200 \\0.1x_1+0.8x_2+0.3x_3\leq750 \\x_1+x_2+x_3\leq575 \\x_1\geq0, x_2\geq0, x_3\geq 0$

From here use computer implementation to solve using the simplex method.

$\\x_1=343.182 \\x_2=231.818 \\x_3=0$

Therefore, the optimal solution will occur when there are 343.182 acres of soy planted and 231.818 acres of corn planted.

The maximum profit at this solution will be, $230,454.50.

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

View Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

View Tutors

Ronald
Certified Tutor

Towson University, Master of Science, Counseling Psychology.

View Tutors

Jonathan
Certified Tutor

East Carolina University, Bachelor of Science, Chemistry. East Carolina University, Bachelor of Science, Biology, General.

Popular Subjects

Math Tutors in Philadelphia, Chemistry Tutors in Philadelphia, Math Tutors in Seattle, Math Tutors in New York City, English Tutors in Los Angeles, Algebra Tutors in Boston, French Tutors in San Diego, Computer Science Tutors in Philadelphia, Statistics Tutors in Miami, ISEE Tutors in Denver

Popular Courses & Classes

GRE Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in New York City, SSAT Courses & Classes in Miami, LSAT Courses & Classes in Miami, SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, LSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Los Angeles, ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

MCAT Test Prep in San Diego, SAT Test Prep in Los Angeles, SSAT Test Prep in Miami, ISEE Test Prep in Phoenix, SSAT Test Prep in San Diego, LSAT Test Prep in Houston, ISEE Test Prep in Boston, GRE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Los Angeles, LSAT Test Prep in Dallas Fort Worth

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

All Math Modeling Resources

Flashcards: Linear Programming

Flashcards: Linear Programming

Flashcards: Linear Programming

Flashcards: Linear Programming

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback:

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores and create your own practice tests:

All Math Modeling Resources

Flashcards: Linear Programming

Flashcards: Linear Programming

Flashcards: Linear Programming

Flashcards: Linear Programming

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Create an account to track your scores
and create your own practice tests: