Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 24.4, Problem 2E
Program Plan Intro
To find the feasible solution for the system of equation.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution.
A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows:
- Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.$0.30 per gram.- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.0.90 per gram.
The dietary needs of the specialty food require a minimum of 30% protein and a maximum of 5% fiber. The farm wishes to determine the optimum ratios of corn and soybeans to produce a feed with minimal costs while maintaining nutritional constraints and ensuring that a minimum of 800 grams of feed is used daily.
Restrictions
1. The total amount of feed should be at least 800 grams per day.2. The feed should contain at least 30% protein…
2. The simplex tableau below is an intermediate step resulted from solving a linear
programming problem using simplex method.
(1) What is the current basic feasible solution? Is the current solution optimal, why?
(2) If the current solution is not optimal, identify the pivot element and complete
Gaussian Elimination for the pivot row and the first row of the tableau in the next
iteration.
Then, answer the following questions: which variables are the basic
variables at iteration 2? Is the solution from Iteration 2 likely to be optimal, and why?
Iteration 1:
Π
x1
x2
x3
s1
s2
s3
s4
s5
constant
1
0
-200
-100
0
0
300
0
0
15000
0
0
10
2
1
0
-16
0
0
200
0
0
4
2
0
1
-8
0
0
100
0
1
0
0
0
0
1
0
0
50
0
0
1
0
0
0
0
1
0
80
0
0
0
1
0
0
0
0
1
150
Iteration 2:
Π
x1
x2
x3
s1
s2
s3
s4
$5
constant
Which of the following algorithms can be used to find the optimal solution of an ILP?(a) Enumeration method;(b) Branch and bound method;(c) Cutting plan method;(d) Approximation method.
Chapter 24 Solutions
Introduction to Algorithms
Ch. 24.1 - Prob. 1ECh. 24.1 - Prob. 2ECh. 24.1 - Prob. 3ECh. 24.1 - Prob. 4ECh. 24.1 - Prob. 5ECh. 24.1 - Prob. 6ECh. 24.2 - Prob. 1ECh. 24.2 - Prob. 2ECh. 24.2 - Prob. 3ECh. 24.2 - Prob. 4E
Ch. 24.3 - Prob. 1ECh. 24.3 - Prob. 2ECh. 24.3 - Prob. 3ECh. 24.3 - Prob. 4ECh. 24.3 - Prob. 5ECh. 24.3 - Prob. 6ECh. 24.3 - Prob. 7ECh. 24.3 - Prob. 8ECh. 24.3 - Prob. 9ECh. 24.3 - Prob. 10ECh. 24.4 - Prob. 1ECh. 24.4 - Prob. 2ECh. 24.4 - Prob. 3ECh. 24.4 - Prob. 4ECh. 24.4 - Prob. 5ECh. 24.4 - Prob. 6ECh. 24.4 - Prob. 7ECh. 24.4 - Prob. 8ECh. 24.4 - Prob. 9ECh. 24.4 - Prob. 10ECh. 24.4 - Prob. 11ECh. 24.4 - Prob. 12ECh. 24.5 - Prob. 1ECh. 24.5 - Prob. 2ECh. 24.5 - Prob. 3ECh. 24.5 - Prob. 4ECh. 24.5 - Prob. 5ECh. 24.5 - Prob. 6ECh. 24.5 - Prob. 7ECh. 24.5 - Prob. 8ECh. 24 - Prob. 1PCh. 24 - Prob. 2PCh. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - Prob. 6P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- What gives rise to the fact that any LP with an optimal solution likewise has an optimal basic feasible solution is not immediately apparent.arrow_forwardQuestion : Part A: Write the Linear Programming equations in standard equality form. Part B: Solve the original Linear programming equations graphically (to scale). Clearly identify the feasible region and, if one or more exist, the optimal solution(s) (provide exact values for x1, X2, and Z). Maximize the objective function Z = -4x1 + 2x2 Subject To constraints: -2x1 + 2x2 s7 X12 2 X1 - 4x2 s 0 2x1 + 2x2 2 10 X1, x2 2 0arrow_forwardThe following figure shows a linear programming problem where the shaded region represents the polytope of feasible solutions, the colored lines represent constraint functions, and the black lines represent the contours of the objective function. Darker lines of the objective function contour represent larger values. It also shows five different points, all of which lie within the polytope. The linear program attempts to find the maximum value. Which point corresponds to a solution of the linear program? 2 (B) 5 1 3 E 4 20 …..arrow_forward
- You have to solve it Using Python Programming language.arrow_forwardConstruct a PYTHON program code for an inequality constraint minimization via logarithm barrier method.(OPTIMIZATION) For this problem minimize –x + /y subject to (x – 5)² + (y – 3)² < 3/2 x < 5 -arrow_forwardThe following table belongs to the optimal solition nit of a Lineer Programming Problem. Obtain the formulation of the initial problem. XI x2 ke -Jig 38 X₁ Xu O 1 O 19 41 14 23 38 xu O O 1 VI 38 A 38 AL A2 (1-38M) (2-19M) 38 19 -3 38 5 L 응급 31 19 19 solution 7' 2 5arrow_forward
- Linear Programming: Graphical Method A. Determine the optimal solution of the following LP problems: Use Desmos Calculator to graph. (Screenshot the graphs and paste here.) Show your complete solution. 1. Maximize: Subject to: Z 4x + 3y ≤ 24 y-x ≤ 4 x, y ≥ 0 = 200x + 350yarrow_forwardSolve the following LPP by graphical Method Maximize Z =22X1+18X2 Subject to constraints: 960X1+640X2≤15 360X1+X2≤20 and X1,X2≥0 (Note the X1 And X2 are variables and not to be mistaken with muliplication symbol)arrow_forwardRounding the solution of a linear programming problem to the nearest integer values provides a(n): a. integer solution that is optimal. b. integer solution that may be neither feasible nor optimal. c. feasible solution that is not necessarily optimal. d. infeasible solution.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole