Define a LP model to minimize the largest absolute deviation

Assignment Help Electrical Engineering

Reference no: EM132134782

Advanced Computational Techniques in Engineering Assignment - Optimisation

For this assignment, you are required to carry out the process of attempting to solve different optimisation problems. For each question, you are required to report your results in details.

Question 1 - Suppose a linear equation is to be fit predicting raw material price as a linear function of the quantity of product A and produce B (made of the same raw material) sold given the following data:

Price of raw material	Quantity of product A sold	Quantity of product B sold
5	9	1
2	13	8
9	17	3
10	8	5
4	10	9
6	15	2

Assume the prediction equation is y_i = c₁x_1i + c₂x_2i, where c₁, c₂ are the prediction parameters on the quantity of products A and B sold, respectively, and c₀ is the intercept. Define x_1i, x_2i as the observations on the quantity of products A and B sold, respectively, and y_i as the observed price. I identifies the i^th observation.

(1) Suppose the desired criterion for equation fit is that the fitted data exhibit minimum of the largest absolute deviation between the raw material price and its prediction.

Please define a LP model to minimize the largest absolute deviation.

Write down the tabular form of the formed LP problem.

Solve the formed LP problem using the MATLAB function-linprog.

(2) Suppose the desired criteria for equation fit is that the fitted data exhibit minimum sum of the squared deviations between the raw material price and its prediction. You are then asked to solve the formed least square (LS) problem.

Write down the linear system equation (Ax=B) of the LS problem.

Solve the LS problem using the normal equations approach.

Question 2 - You have certain types of chicken wire to build a temporary enclosure for holding chicken at your backyard. You plan to build a rectangular enclosure (see Figure 1)

You have 50m of Type-1 chicken wire, and you want to maximise the area of the enclosure for your given materials.

Please find the lengths of rectangular sides x1, x2 using the Lagrange Multipliers method. (suggestion: consider a two dimensional (2D) optimisation procedure)

Please find the rectangular sides x1, x2 using the Golden Section Search method. Please provide your matlab code. (Suggestion: please convert the 2D optimisation problem to a 1D optimisation problem using the relationship: 2*(x1+x2) = 50 → x2 = 25-x1.

Please find the rectangular sides x1, x2 using the Newton's Method. Please provide your matlab code.

Reference no: EM132134782

Questions Cloud

Implement in java an efficient algorithm : Implement in Java an efficient algorithm that decides if a number x is in the matrix. Please include in the header of your Java program /

What was the nominal return on the investment : The inflation rate over the past year was 4.2 percent. If an investment had a real return of 9.4 percent, what was the nominal return on the investment?

Six-month return on transaction : If the price of the stock increases to ?$102 within six? months, the? six-month return on this transaction is ?%. ? (Round to two decimal? places.)

Create a program that will build a binary search tree : Create a program that will build a binary search tree (BST) by adding new elements one at a time.

Define a LP model to minimize the largest absolute deviation : Engg7302 Advanced Computational Techniques in Engineering Assignment - Optimisation, The University of Queensland, Australia. define a LP model

Complete produce a project plan : Complete produce a project plan which results in the development of a major software product to solve a customer problem, for a Course Registration System.

Set up and solve a valuation : Set up and solve a valuation for thew following non-constant growth stock:

Explain the systematic risk principle : Explain the systematic risk principle and how it relates to beta. according to the below message

What are the worst case and best case running times : What are the worst case and best case running times for this sorting algorithm? Give concrete examples on when that happens.

Reviews

len2134782

10/8/2018 5:50:24 AM

This assignment is worth 20% of the total marks for the course. For this assignment, you are required to carry out the process of attempting to solve different optimisation problems. For each question, you are required to report your results in details. It should include your best solution and its corresponding solution procedures. If you are asked to solve those sub-questions using MATLAB, then their MATLAB source code is required. Marks will be awarded based on how well your submission addresses the above points. Where to submit: Submit the assignment report via the Blackboard turnitin assignment submission system.

Write a Review

Required(*) Message

User Account

All Pages