We are open Saturday and Sunday!

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: Computational Methods

Using Newton's Method as the computational method, optimize the follow problem.

A cow that weighs 175 pounds gains 3 pounds per day, and it costs 30 cents per day to keep that cow. The market price for cows is 75 cents per pound, but the price is falling one cent per day. When should the cow be sold to make the maximum profit?

It is recommended to wait 8 or 9 days to sell the cow. This should result in a net profit of $132.90.

It is recommended to wait 9 or 10 days to sell the cow. This should result in a net profit of $132.

It is recommended to wait 6 or 7 days to sell the cow. This should result in a net profit of $130.

It is recommended to wait 7 or 8 days to sell the cow. This should result in a net profit of $131.90.

It is recommended to wait 2 or 5 days to sell the cow. This should result in a net profit of $131.90.

Report an Error Copyright Notice

Flashcards: Computational Methods

Using Newton's Method as the computational method, optimize the follow problem.

Your answer:

It is recommended to wait 8 or 9 days to sell the cow. This should result in a net profit of $132.90.

Your answer:

It is recommended to wait 9 or 10 days to sell the cow. This should result in a net profit of $132.

Your answer:

It is recommended to wait 6 or 7 days to sell the cow. This should result in a net profit of $130.

Your answer:

It is recommended to wait 2 or 5 days to sell the cow. This should result in a net profit of $131.90.

Correct answer:

It is recommended to wait 7 or 8 days to sell the cow. This should result in a net profit of $131.90.

Explanation:

Assume that the growth rate of the cow is proportional to its weight.

In mathematical terms:

$\frac{dw}{dt}=cw$

Looking at the known information,

Variables:

$\\t=\text{time (days)} \\w=\text{weight (lbs)} \\p=\text{proft (}\$\text{/lbs)} \\C=\text{cost to keep the cow} \\R=\text{revenue} \\P=\text{profit}$

Therefore,

$\frac{dw}{dt}=3\text{ lbs/day}$

when

$w=175\text{ lbs}$

$\frac{dw}{dt}=cw, w(0)=175$

$c=\frac{3}{175}=0.017$

Thus the differential equation to solve for is as follows.

$\frac{dw}{dt}=0.017w, w(0)=175$

Solving by separation of variables results in the following equation.

$w=175e^{0.017t}$

From here, formulate the model with the new weight equation.

$\\y=f(x) \\y=(0.75-0.01t)(175e^{0.017t})-0.30t$

Recall that the goal is to optimize the question over

$S=\begin{Bmatrix} x:x\geq0 \end{Bmatrix}$ .

Use a graphing calculator or computer technology to graph the function.

Screen shot 2016 04 27 at 9.31.27 am

Observing the graph it appears the maximum profit for the cow occurs around x=7 and y=131.9 .

From here, answer the question. Taking into account the growth rate of the cow is still increasing, it is recommended to wait 7 or 8 days to sell the cow. This should result in a net profit of $131.90.

Flashcards: Computational Methods

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.

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

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

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

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

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

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

Report an Error Copyright Notice

Flashcards: Computational Methods

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:

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

Your answer:

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

Your answer:

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

Your answer:

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

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.

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

Grace
Certified Tutor

University of Evansville, Bachelor of Science, Archaeology.

View Tutors

Donald
Certified Tutor

Bowling Green State University-Main Campus, Bachelor of Science, Geology. Bowling Green State University-Main Campus, Master ...

View Tutors

Thomas
Certified Tutor

California State University-Dominguez Hills, Bachelor in Arts, Studio Arts. University of California-San Diego, Doctor of Phi...

Popular Subjects

Algebra Tutors in Seattle, GRE Tutors in Dallas Fort Worth, Math Tutors in Boston, GRE Tutors in San Francisco-Bay Area, GRE Tutors in Seattle, MCAT Tutors in Miami, Statistics Tutors in New York City, Statistics Tutors in San Diego, Statistics Tutors in Denver, Calculus Tutors in Washington DC

Popular Courses & Classes

GRE Courses & Classes in Los Angeles, SSAT Courses & Classes in Seattle, GMAT Courses & Classes in Atlanta, ACT Courses & Classes in New York City, Spanish Courses & Classes in Chicago, ISEE Courses & Classes in San Diego, MCAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Seattle, SAT Courses & Classes in Philadelphia, ACT Courses & Classes in Miami

Popular Test Prep

ISEE Test Prep in San Diego, MCAT Test Prep in Phoenix, SSAT Test Prep in New York City, ISEE Test Prep in Boston, GRE Test Prep in Phoenix, SSAT Test Prep in Washington DC, SSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in New York City, SAT Test Prep in Los Angeles, ACT Test Prep in Phoenix

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: Computational Methods

Flashcards: Computational Methods

Flashcards: Computational Methods

Flashcards: Computational Methods

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: Computational Methods

Flashcards: Computational Methods

Flashcards: Computational Methods

Flashcards: Computational Methods

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: