Explanation Given: The given conditions are, 3 x + 4 y ≤ 42 x + y ≤ 12 2 x + y ≤ 20 x ≥ 0 , y ≥ 0 Approach: (1) If all the entries are nonnegative, the optimal solution has been reached. (2) If there is one or more negative entries, the optimal solution has not been reached. Calculation: Consider the given equations. P = 3 x + 2 y Introduce the slack variables, u , v , w and rewrite the objective function in the standard form that gives the system of linear equation as follows, 3 x + 4 y + u = 42 x + y + v = 12 2 x + y + w = 20 − 5 x − 3 y + P = 0 The initial simplex table is as follows, x y u v w P Constant 3 4 1 0 0 0 42 1 1 0 1 0 0 12 2 1 0 0 1 0 20 − 5 − 3 0 0 0 1 0 Some of the elements in the last row are negative, so it is not in final form. Select the pivot row, pivot element and column for further simplification. x y u v w P Constant Ratio 3 4 1 0 0 0 42 14 1 1 0 1 0 0 12 12 ( 2 ) 1 0 0 1 0 20 10 − 5 − 3 0 0 0 1 0 Apply the row operation R 3 → R 3 2 . x y u v w P Constant 3 4 1 0 0 0 42 1 1 0 1 0 0 12 1 1 2 0 0 1 2 0 10 − 5 − 3 0 0 0 1 0 Apply the row operation R 1 → R 1 − 3 R 3 , R 2 → R 2 − R 3 and R 4 → R 4 + 5 R 3 x y u v w P Constant Ratio 0 5 2 1 0 − 3 2 0 12 4

12th Edition

ISBN: 8220103649001

Author: Tan

Publisher: CENGAGE L

See similar textbooks

Videos

Question

Chapter 4.CRE, Problem 4CRE

To determine

To maximize:

The objective function P=5x+3y by simplex method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.CRE, Problem 3CRE

Chapter 4.CRE, Problem 5CRE

Students have asked these similar questions

i) Consider the set S = {−6, −3, 0, 3, 6}. Draw a graph G whose set of verti- ces be S and such that for i, j ∈ S, ij ∈ E(G) if ij are related to a rule that t'u you choose to apply to i and j. (ii) A graph G of order 12 has as a set of vertices c1, c2, . . . , c12 for the do- ce configurations of figure 1. A movement on said board corresponds to moving a coin to an unoccupied square using the following two rules: 1. the gold coin can move only horizontally or diagonally, 2. the silver coin can move only vertically or diagonally. Two vertices ci, cj, i̸ = j are adjacent if it is possible to move ci to cj in a single movement. a) What vertices are adjacent to c1 in G? b) Draw the subgraph induced by {c2, c6, c9, c11}

2. Find the exact value of 12 + 12+12+√√12+ √12+ 12

he following contingency table details the sex and age distribution of the patients currently registered at a family physician's medical practice. If the doctor sees 17 patients per day, use the binomial formula and the information contained in the table to answer the question: SEX AGE Under 20 20-39 40-59 60-79 80 or over TOTAL Male 5.6% 12.8% 18.4% 14.4% 3.6% 54.8% Female 2.8% 9.6% 13.2% 10.4% 9.2% 45.2% TOTAL 8.4% 22.4% 31.6% 24.8% 12.8% 100.0% if the doctor sees 6 male patients in a day, what is the probability that at most half of them are aged under 39?

Chapter 4 Solutions

EBK FINITE MATHEMATICS FOR THE MANAGERI

Ch. 4.1 - Give the three characteristics of a standard...Ch. 4.1 - a. When the initial simplex tableau is set up, how...Ch. 4.1 - In the simplex method, how is a pivoted column...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - In Exercises 1-6, a write the linear programming...Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-16, determine whether the given...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

To maximize: The objective function P = 5 x + 3 y by simplex method.

Solution Summary: The author explains how to maximize the objective function P=5x+3y by simplex method.

Videos

To maximize:

The objective function P=5x+3y by simplex method.

Want to see the full answer?

Chapter 4 Solutions

To maximize: The objective function P = 5 x + 3 y by simplex method.

Solution Summary: The author explains how to maximize the objective function P=5x+3y by simplex method.

Videos

To maximize: The objective function P=5x+3y by simplex method.

Want to see the full answer?

Chapter 4 Solutions

To maximize:

The objective function P=5x+3y by simplex method.