4.1 Solve the linear programming problem using the Simplex method: ### Solving Linear Programming Problems using the Simplex Method#### Objective:Maximize \( P = x + 2y - z \)#### Subject to Constraints:1. \( 2x + y + z \leq 14 \)2. \( 4x + 2y + 3z \leq 28 \)3. \( 2x + 5y + 5z \leq 30 \)4. \( x \geq 0, y \geq 0, z \geq 0 \)#### Simplex Tableau Initialization:\[ \begin{array}{|c|c|c|c|c|c|c|c|}\hline & x & y & z & u & v & w & P & c \\\hline\text{Start:} & 2 & 1 & 1 & 1 & 0 & 0 & 0 & 14 \\ & 4 & 2 & 3 & 0 & 1 & 0 & 0 & 28 \\ & 2 & 5 & 5 & 0 & 0 & 1 & 0 & 30 \\\hline\text{} & -1 & -2 & 1 & 0 & 0 & 0 & 1 & 0 \\\hline\end{array}\]#### Solution Extraction:Please fill out the following once you've computed the solution:- \( X = \_\_\_\_\_\_\_\_ \)- \( Y = \_\_\_\_\_\_\_\_ \)- \( Z = \_\_\_\_\_\_\_\_ \)- \( P = \_\_\_\_\_\_\_\_ \)#### Visual Description of the Tableau:The table above is a standard initial simplex tableau for solving the given linear programming problem. It includes:- Decision variables \(x\), \(y\), and \(z\).- Slack variables \(u\), \(v\), and \(w\) added to convert inequalities to equalities.- The column for the objective function \(P\), and - The constants column \(c\) representing the right-hand side of the inequalities.#### Instructions:1. Identify the pivot element to enter the basis.2. Perform the row operations to update the tableau.3

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Solve the linear programming Maximize: P = x + 2y-z Verify your Solution Start: X2424 11252 -1 -2 73551 EHOOO 1 0 0 1 0 OOTOK 0 1 0 problem using the Simplex method: W 0 0 1 0 Subject to: 1. 2x+y+z≤ 14 (constraints) 2. 4x + 2y + 3zs 28 3. 2x + 5y + 5z ≤ 30 4. x ≥ 0, y ≥ 0, z 20 0 0 0 1 14 28 130 10

Solve the linear programming Maximize: P = x + 2y-z Verify your Solution Start: X2424 11252 -1 -2 73551 EHOOO 1 0 0 1 0 OOTOK 0 1 0 problem using the Simplex method: W 0 0 1 0 Subject to: 1. 2x+y+z≤ 14 (constraints) 2. 4x + 2y + 3zs 28 3. 2x + 5y + 5z ≤ 30 4. x ≥ 0, y ≥ 0, z 20 0 0 0 1 14 28 130 10

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.CR: Chapter Review

Problem 70E: A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three...

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