Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 24.4, Problem 2E
Program Plan Intro

To find the feasible solution for the system of equation.

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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.
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