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2 years ago

2. Max z = 3X1 + 5X2+ 4X3 S.t.2X1 +3X2 ≤ 18 2X1 + X2 ≤ 10 3X1 + 2X+4X3 ≤ 15 X1, X2, X3 ≥ 0

Business

1 answer:

lions [1.4K]2 years ago

7 0

The interpretation of the result is that the maximum value of the objective function is 29

<h3>How to solve and interpret the result?</h3>

The objective function is given as:

Max z = 3x₁ + 5x₂+ 4x₃

The constraints are:

2x₁ +3x₂ ≤ 18

2x₁ + x₂ ≤ 10

3x₁ + 2x₂ +4x₃ ≤ 15

x₁, x₂, x₃ ≥ 0

Subtract the second inequality from the first

2x₁ - 2x₁ + 3x₂ - x₂ ≤ 18 - 10

Evaluate the like terms

2x₂ ≤ 8

Divide by 2

x₂ ≤ 4

Substitute 4 for x₂ in 2x₁ +3x₂ ≤ 18

2x₁ +3*4 ≤ 18

This gives

2x₁ + 12 ≤ 18

Evaluate the like terms

2x₁ ≤ 6

Divide by 2

x₁ ≤ 3

Substitute 4 for x₂ and 3 for x₁ in 3x₁ + 2x₂ +4x₃ ≤ 15

3*3 + 2*4 +4x₃ ≤ 15

This gives

17 +4x₃ ≤ 15

Evaluate the like terms

4x₃ ≤ -2

Divide by 4

x₃ ≤ -0.5

From the constraints, we have:

x₁, x₂, x₃ ≥ 0

So, we set all negative values to 0

This means that:

x₃ ≤ 0

Substitute these values in the objective function

Max z = 3 * 3 + 5 * 4 + 4 * 0

Evaluate

Max z = 29

Hence, the interpretation of the result is that the maximum value is 29

Read more about objective functions at:

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