Explanation Given: The given problem is, Maximize P = 2 x + y + z subject to x + 2 y + 3 z ≤ 28 2 x + 3 y − z ≤ 6 x − 2 y + z ≥ 4 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. Calculation: Consider the given linear programming problem. Change all the constraints signs as ≤ . Maximize P = 2 x + y + z subject to x + 2 y + 3 z ≤ 28 2 x + 3 y − z ≤ 6 − x + 2 y − z ≤ − 4 x ≥ 0 , y ≥ 0 , z ≥ 0 Introduce the slack variables u v and w in the given linear programming problem, x + 2 y + 3 z + u = 28 2 x + 3 y − z + v = 6 − x + 2 y − z + w = − 4 − 2 x − y − z + P = 0 The initial simplex tableau is, x y z u v w P Constant 1 2 3 1 0 0 0 28 ( 2 ) 3 − 1 0 1 0 0 6 − 1 2 − 1 0 0 1 0 − 4 − 2 − 1 − 1 0 0 0 1 0 Table ( 1 ) At x = 0 , y = 0 , z = 0 we have u = 28 , v = 6 , w = − 4 , P = 0 In the initial simplex tableau the minimum value for bottom row is − 2 so pivot this column, The pivoted element is 2 and apply 1 2 R 2 . x y z u v w P Constant 1 2 3 1 0 0 0 28 ( 1 ) 3 2 − 1 2 0 1 2 0 0 3 − 1 2 − 1 0 0 1 0 − 4 − 2 − 1 − 1 0 0 0 1 0 Table ( 2 ) Now apply R 1 − R 2 , R 3 + R 2 and R 4 + 2 R 2

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Chapter 4.3, Problem 17E

To determine

To solve:

The given linear programming problem.

Maximize P=2x+y+z

subject to x+2y+3z≤28 2x+3y−z≤6 x−2y+z≥4 x≥0,y≥0,z≥0

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Chapter 4.3, Problem 16E

Chapter 4.3, Problem 18E

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Chapter 4 Solutions

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The given linear programming problem. Maximize P = 2 x + y + z subject to x + 2 y + 3 z ≤ 28 2 x + 3 y − z ≤ 6 x − 2 y + z ≥ 4 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains that the optimal solution for linear programming problem is x=467,y=0,z=

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To solve:

The given linear programming problem.

Maximize P=2x+y+z

subject to x+2y+3z≤28 2x+3y−z≤6 x−2y+z≥4 x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

The given linear programming problem. Maximize P = 2 x + y + z subject to x + 2 y + 3 z ≤ 28 2 x + 3 y − z ≤ 6 x − 2 y + z ≥ 4 x ≥ 0 , y ≥ 0 , z ≥ 0

Solution Summary: The author explains that the optimal solution for linear programming problem is x=467,y=0,z=

Videos

To solve: The given linear programming problem. Maximize P=2x+y+z subject to x+2y+3z≤28 2x+3y−z≤6 x−2y+z≥4 x≥0,y≥0,z≥0

Want to see the full answer?

Chapter 4 Solutions

To solve:

The given linear programming problem.

Maximize P=2x+y+z

subject to x+2y+3z≤28 2x+3y−z≤6 x−2y+z≥4 x≥0,y≥0,z≥0