Explanation Given: The given problem is, Minimize C = 3 x + 2 y + z subject to x + 2 y + z ≤ 20 3 x + y ≤ 30 2 x + y + z = 10 x ≥ 0 , y ≥ 0 , z ≥ 0 Approach: 1. In the standard maximization problem the objective function is to be maximized. 2. All variable involved in the problem should be non-negative. 3. Each linear constraint may be written so that the expression involving the variables is less than or equal to a non-negative constraint. 4. The optimal solution is reached when all the entries of bottom row of the simplex tableau are non-negative. Calculations: Consider the given linear programming problem. Rewrite them problem as maximization problem with P = − C . Maximize P = − 3 x − 2 y − z subject to x + 2 y + z ≤ 20 3 x + y ≤ 30 2 x + y + z = 10 x ≥ 0 , y ≥ 0 , z ≥ 0 The constraint 2 x + y + z = 10 involves two constraints. 2 x + y + z ≤ 10 2 x + y + z ≥ 10 Change all the constraints signs as ≤ . Maximize P = − 3 x − 2 y − z

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Author: Tan

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Chapter 4.3, Problem 20E

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To solve:

The given linear programming problem.

Minimize C=3x+2y+z

subject to x+2y+z≤20 3x+y ≤30 2x+y+z=10 x≥0,y≥0,z≥0

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Chapter 4.3, Problem 19E

Chapter 4.3, Problem 21E

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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...

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The given linear programming problem. Minimize C = 3 x + 2 y + z subject to x + 2 y + z ≤ 20 3 x + y ≤ 30 2 x + y + z = 10 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains that the linear programming problem has no optimal solution. The objective function is to be maximized in the standard maximization problem.

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To solve:

The given linear programming problem.

Minimize C=3x+2y+z

subject to x+2y+z≤20 3x+y ≤30 2x+y+z=10 x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

The given linear programming problem. Minimize C = 3 x + 2 y + z subject to x + 2 y + z ≤ 20 3 x + y ≤ 30 2 x + y + z = 10 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains that the linear programming problem has no optimal solution. The objective function is to be maximized in the standard maximization problem.

Videos

To solve: The given linear programming problem. Minimize C=3x+2y+z subject to x+2y+z≤20 3x+y ≤30 2x+y+z=10 x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

To solve:

The given linear programming problem.

Minimize C=3x+2y+z

subject to x+2y+z≤20 3x+y ≤30 2x+y+z=10 x≥0,y≥0,z≥0