Explanation Given information: The objective function which has to maximize is: M = 2 x + 5 y which is subjected to the constraints: { x + y ≤ 7 4 x + 3 y ≤ 24 x ≥ 0 y ≥ 0 Formula used: The maximization problem of simplex can be solved as below: Step 1: Write the initial tableau and find the feasible solution. Step 2: Find the pivot column, by finding maximum negative number in the last row of the tableau. Step 3: Now divide the all elements which are in the last column by their corresponding elements of pivot column to decide pivot elements. Step 4: Now to make the pivot element unity, divide all the element of pivot row by 1 and make all other elements of pivot column to zero by row operation. Step 5: If there is one or more than one negative number in the last row, then the above tableau is not optimal, it needs iteration. Calculation: Write the provided constraints in the form of linear equations by introducing slack variables, u , and v which are: x + y + u = 7 4 x + 3 y + v = 24 − 2 x − 5 y + M = 0 Step 1: Write the initial tableau and find the feasible solution. In the matrix form it can be written as: x y u v M [ 1 1 1 0 0 7 4 3 0 1 0 24 − 2 − 5 0 0 1 0 ] So, the above simplex tableau is initial tableau, therefore one feasible solution is: x = 0 , y = 0 , u = 7 , v = 24 and M = 0 Step 2: Find the pivot column, by finding maximum negative number in the last row of the tableau. From the above table it can be observed that in the last row the maximum negative number is − 5 so the 2 nd column is pivot column. Step 3: Now divide the all elements which are in the last column by their corresponding elements of pivot column to decide pivot elements. u v M [ 1 1 1 0 0 7 4 3 0 1 0 24 − 2 − 5 0 0 1 0 ] 7 1 = 7 24 3 = 8 It can be observed that the minimum positive ratio is 7 which is 1 st row, therefore the pivot element is 1 st row and 2 nd column, which is 1

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4, Problem 2RE

To determine

To calculate: The maximum value of objective function: M=2x+5y which is subjected to the constraints:

{x+y≤74x+3y≤24x≥0y≥0

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 1RE

Chapter 4, Problem 3RE

Students have asked these similar questions

Two functions ƒ and g are defined in the figure below. g 6 6 7 8 8 8 9 Domain of f Range of f Domain of g Range of g Find the domain and range of the composition g.f. Write your answers in set notation. (a) Domain of gof: (b) Range of gof: ☐ ☑ 0,0,...

The table below shows the estimated effects for a logistic regression model with squamous cell esophageal cancer (Y = 1, yes; Y = 0, no) as the response. Smoking status (S) equals 1 for at least one pack per day and 0 otherwise, alcohol consumption (A) equals the average number of alcohoic drinks consumed per day, and race (R) equals 1 for blacks and 0 for whites. Variable Effect (β) P-value Intercept -7.00 <0.01 Alcohol use 0.10 0.03 Smoking 1.20 <0.01 Race 0.30 0.02 Race × smoking 0.20 0.04 Write-out the prediction equation (i.e., the logistic regression model) when R = 0 and again when R = 1. Find the fitted Y S conditional odds ratio in each case. Next, write-out the logistic regression model when S = 0 and again when S = 1. Find the fitted Y R conditional odds ratio in each case.

The chi-squared goodness-of-fit test can be used to test if data comes from a specific continuous distribution by binning the data to make it categorical. Using the OpenIntro Statistics county_complete dataset, test the hypothesis that the persons_per_household 2019 values come from a normal distribution with mean and standard deviation equal to that variable's mean and standard deviation. Use signficance level a = 0.01. In your solution you should 1. Formulate the hypotheses 2. Fill in this table Range (-⁰⁰, 2.34] (2.34, 2.81] (2.81, 3.27] (3.27,00) Observed 802 Expected 854.2 The first row has been filled in. That should give you a hint for how to calculate the expected frequencies. Remember that the expected frequencies are calculated under the assumption that the null hypothesis is true. FYI, the bounderies for each range were obtained using JASP's drag-and-drop cut function with 8 levels. Then some of the groups were merged. 3. Check any conditions required by the chi-squared…

Chapter 4 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 4.1 - 1. Determine by inspection a particular solution...Ch. 4.1 - Prob. 2CYU Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - 712For each of the linear programming problems in...Ch. 4.1 - 7–12 For each of the linear programming problems...

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.

The maximum value of objective function: M = 2 x + 5 y which is subjected to the constraints: { x + y ≤ 7 4 x + 3 y ≤ 24 x ≥ 0 y ≥ 0

Solution Summary: The author explains how the maximization problem of simplex can be solved by writing the initial tableau and finding the feasible solution.

Videos

To calculate: The maximum value of objective function: M=2x+5y which is subjected to the constraints:

{x+y≤74x+3y≤24x≥0y≥0

Want to see the full answer?

Chapter 4 Solutions

The maximum value of objective function: M = 2 x + 5 y which is subjected to the constraints: { x + y ≤ 7 4 x + 3 y ≤ 24 x ≥ 0 y ≥ 0

Solution Summary: The author explains how the maximization problem of simplex can be solved by writing the initial tableau and finding the feasible solution.

Videos

To calculate: The maximum value of objective function: M=2x+5y which is subjected to the constraints: {x+y≤74x+3y≤24x≥0y≥0

Want to see the full answer?

Chapter 4 Solutions

To calculate: The maximum value of objective function: M=2x+5y which is subjected to the constraints:

{x+y≤74x+3y≤24x≥0y≥0