Identify the vertices of the feasible region and use them to find the maximum and/or minimum value for the given linear programm

Question

1 year ago

14

ing constraints.
System of Linear Programming:

z=−3x+5y

x+y≥−2

3x−y≤2

x−y≥−4

Maximum value of z:

Minimum value of z

1 answer:

Ghella [55] · Answer 1 · 2023-08-17T02:07:15+03:00

The maximum value of the objective function is 26 and the minimum is -10

<h3>How to determine the maximum and the minimum values?</h3>

The objective function is given as:

z=−3x+5y

The constraints are

x+y≥−2

3x−y≤2

x−y≥−4

Start by plotting the constraints on a graph (see attachment)

From the attached graph, the vertices of the feasible region are

(3, 7), (0, -2), (-3, 1)

Substitute these values in the objective function

So, we have

z= −3 * 3 + 5 * 7 = 26

z= −3 * 0 + 5 * -2 = -10

z= −3 * -3 + 5 * 1 =14

Using the above values, we have:

The maximum value of the objective function is 26 and the minimum is -10

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