User Account

All Pages

Find the dimension of the rectangle to maximize the area

Assignment Help Mathematics
Reference no: EM131012971

1. A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be enclosed with a protective fence. If there are 12 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary.

2. The rectangular bird sanctuary with one side along a straight river is to be constructed so that it contains 8 km2 of area. Find the dimensions of the rectangle to minimize the amount of fence necessary to enclose the remaining three sides.

3. Find two positive real numbers such that the sum of the first number squared and the second number is 48 and their product is a maximum.

4. Find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximum.

5. A wire of length 12 m is divided into two pieces and the pieces are bent into a square and a circle. How should this be done in order to minimize the sum of their areas?

6. Find the positive number x such that the sum of x and its reciprocal is as small as possible. Does this problem require optimization over an open interval or a closed interval?

7. Find two positive real numbers such that they add to 40 and their product is as large as possible.

Verified Expert

The specified 7 problems are of Maxima-Minima problems. Some of them are directly based on the theory. They are solved by applying the theories of maxima and minima of a function of single variable. Problem no 3,4,6,7 are of this type. While the problems no 1,2 and 5 are practical problems which are needed to be converted into a mathematical model and then they are solved applying the theory.

Reference no: EM131012971

Questions Cloud

Calculate the modulus of resilience : A cylindrical specimen of stainless steel having a diameter of 12.8 mm and a gauge length of 50.8 mm is pulled in tension. In the linear elastic region, a stress of 400 MPa corresponds to a strain of 0.002. Furthermore, the 0.002 strain offset li..
Determine the square footage of your house : How do you determine the correct number of significant figures to use for each distance measurement? Be specific.(pacing,EDm, GPS and tape), Which measurement method would you choose to determine the square footage of your house? Why would you choos..
Determine vertical component of the reaction ay : Determine vertical component of the reaction Ay at the pinned support A if applied moment M is 82 lb-ft and the weight of the cylinder is 43 lb. Sign convention is upward positive and downward negative. Be sure to include units in pounds as part ..
How long was the detour in yard : On a 1 mile walking tour to new york city a group had to take a detour that was 100 yard shorter than half the distance of the tour how long was the detour in yard
Find the dimension of the rectangle to maximize the area : The remaining three sides are to be enclosed with a protective fence. If there are 12 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary.
Determine the largest screw spacing for the pi-shaped beams : Determine the largest screw spacing for the pi-shaped beams that allows the beams to carry an ultimate shear load of V = 2000 lbs. Each screw can support 350 lbs.
Calculate diluted earnings per share : Calculate diluted earnings per share for 2013 and the incremental EPS of the preferred stock and convertible bonds. If required, round your answers to the nearest cent.
Free-rider problem aggravate adverse selection : Would you be more willing to lend to a friend if she put all of her life saving into her business than you would if she had not done so? Why? Wealthy people often worry that others will seek to marry them only for their money. Is this a problem of ..
Determine the force p required to move the wedge : Determine the force P required to move the wedge under the beam. The coefficient of static friction between the beam and the wedge is 0.3 and the wedge and the support surface at B is 0.35. Neglect the size of the wedge and the thickness of the be..

Reviews

Write a Review

Mathematics Questions & Answers

  Questions on ferris wheel

Prepare a Flexible Budget Gator Divers is a company that provides diving services such as underwater ship repairs to clients in the Tampa Bay area.

  Logistic map

This assignment has two question related to maths. Questions are related to bifurcation cascade and logistic map.

  Finding the probability of cards

This assignment has questions related to probabiltiy.

  Systems of ode

Find all the xed points, and study their stability and Draw the phase portrait of the system, as well as the graphs of the solutions in all relevant cases.

  Derive the boolean expression

Derive the Boolean Expression and construct the switching circuit for the truth table stated

  System of equations

Evaluate which equations are under-identified, just-identified, and over-identified.

  Linear programming problem

Linear programming problem consisting of only two constraints with one objective function.

  Find the natural domain

Find the natural domain of the given functions.

  Introduction to numerical methods

Compute the coecients of the polynomials using the term recurrence relation.

  Chart of the topological manifold

De?nition of smoothness of functions on a smooth manifold is chart independent and hence geometric.

  Mathematics in computing

Questions related on mathematics in computing.

  Complex problems

Complex problems

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

Submit Assignment

Academics

Major Subjects

Majors

Get In Touch

whatsapp: +1-415-670-9521

Phone: +1-415-670-9521

Email: [email protected]

TERMS & POLICIES

HELP & SUPPORT

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd