Use the simplex method and the Duality Principle to solve the following minimum problem: (see image below)and using your final tableau answer the questions below by entering the correct answer in each blank box. ### Problem Statement**Objective:**Minimize the function: $ C = 2x_1 + 3x_2 $**Subject to the constraints:**\[\begin{align*}4x_1 - x_2 & \geq 2 \\x_1 + x_2 & \geq 1 \\x_1 & \geq 0 \\x_2 & \geq 0\end{align*}\]### Explanation:- **Objective Function**: The function $ C = 2x_1 + 3x_2 $ is the expression to be minimized.- **Constraints**: These inequalities restrict the values of $ x_1 $ and $ x_2 $ to feasible solutions that satisfy all conditions. - The first inequality $ 4x_1 - x_2 \geq 2 $ represents a linear constraint. - The second inequality $ x_1 + x_2 \geq 1 $ is another linear constraint. - The last two constraints $ x_1 \geq 0 $ and $ x_2 \geq 0 $ ensure that the variables are non-negative, which is typical in linear programming problems. **Note**: The problem can be graphically interpreted by plotting the constraints on a Cartesian plane, where the feasible region will be the intersection of all half-planes represented by the inequalities. The optimal solution will be found at a vertex (corner point) of this feasible region.

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Use the simplex method and the Duality Principle to solve the following minimum problem: (see image below) and using your final tableau answer the questions below by entering the correct answer in each blank box.

Use the simplex method and the Duality Principle to solve the following minimum problem: (see image below) and using your final tableau answer the questions below by entering the correct answer in each blank box.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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