Question: Find the rectangle with maximal area which can be cut from an elliptical plate (see the figure below). The long axis of the ellipse is

Find the rectangle with maximal area which can be cut from an elliptical plate (see the figure
below). The long axis of the ellipse is 3 meters and the short axis is 1 meter, so the equation of
the ellipse is given by ( x^2 )/9 + y^2 =1

(1) Develop the mathematical model of the optimisation problem;
(2) Solve the problem using Lagrange Multiplier method.
(3) Use MATLAB fmincon or Excel solver to solve the problem.

y X

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

The new line character is utilized solely as the last person in each message. On association with the server, a client can possibly (I) question the situation with a client by sending the client's...

Design a Java class that represents a cache with a fixed size. It should support operations like add, retrieve, and remove, and it should evict the least recently used item when it reaches capacity.

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

Find the rectangle with maximal area which can be cut from an elliptical plate (see the figure below). The long axis of the ellipse is 3 meters and the short axis is 1 meter , so the equation of the...

y X X A rancher has 600 feet of fencing with which to construct adjacent, equally sized rectangular pens as shown in the figure above. What dimensions should these pens have to maximize the enclosed...

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

Complete the following Carolina Biological Lab: Kinematics. Please read the Distance Learning Lab Safety Agreement. By taking part in these labs, you agree to the terms in the Distance Learning...

Table 1. A B C D E F G Mass Math Energy Angle Mass Determined Long Axis | Short Axis Illuminance Determined Area (g) Area (my) (L) (S) Area (my) (Watts/m-) (lux) 90 0. 12 0.045m 0. 045 m 80 O. 1 0....

Rev.Confirming Pages C H A P T E R 7 Planning, Composing, and Revising Chapter Outline The Ways Good Writers Write Activities in the Composing Process Using Your Time Effectively Brainstorming,...

*solve the attached4 questions. 15. Let /(x) =e-2' (a) Find any horizontal and vertical asymptotes of f(r). (b) Find the intervals where f(7) is increasing and the intervals where f (7) is...

Daniel Jackson has just purchased some equipment for his landscaping business. For this equipment he must pay the following amounts at the end of each of the next five years: $10,520, $7,570, $9,370,...

Cash flow analysis. Kary Kinnard has an opportunity to open a franchised pizza outlet. He can lease the building, so he needs to invest only in equipment, which he estimates will cost $60,000. For...

an. c. Musk does not want to have to meet all the requirements necessary for a public stock offering. Which exemption from the public offering registration requirements of the Securities Act of 1933...

2. A company makes three products and has 4 available manufacturing plants. The production time (in minutes) per unit produced varies from plant to plant as shown below: Product 1 Product WNI 2 3 1...

3. Solve the following linear program using the fundamental theorem. Specif- ically, find all vertices of the feasible region, calculate the values of the objective function at those points, and...

13. What is the value of index at the end of this program? public static void main(String [] args) ( for (int index ( System.out.print ln ("The value of index } } // end met hod main } // end class...

C. / d. Names of methods and variable should always start with: 8. upper case letter and upper case for all subsequent words . b. lower case letter and lower case for all subsequent words it does not...

df(x) The first derivative of a function f(x) at a point x = xo can be approx- dx imated with the two-point central difference formula: df(x) _ f(x+h)-f(xo-h) dx 2h Where h is a small number. Write a...

A firm has total assets of $ 1 0 0 and total debt of $ 2 5 . Equity is $ 7 5 . Debt - equity ratio is 3 . Debt ratios is 2 5 % . Equity ratio is 7 5 % .

The town of Hillside has a surface reservoir that supplies water to the homes in the towns central residential district. A committee of residents is concerned about the systems capacity and wants to...

Consider the example of the town of Lincoln, which was analyzed using a multiplicative model in Figure 7.14. Repeat the forecasts using the additive model, with the same smoothing constants. FIGURE...

Delta Electric Service is an electrical-utility company serving parts of several states. It is considering replacing some of its equipment at generating substations and is trying to decide whether it...

Suppose a monopolist discovers a way to perfectly price discriminate. What is consumer surplus under this scenario? What are the efficiency costs?

Suppose there are three types of consumers who attend concerts at your universitys performing arts center: students, staff, and faculty. Each of these groups has a different willingness to pay for...

Suppose a city has a chain of fitness centers (gyms) all owned by the same company, Fit Fun. A new company is considering opening a gym in the city. Give an example of an aggressive tactic Fit Fun...