Question

Instructions: Identify the vertices of the feasible region and use them to find the maximum and/or minimum value for the given linear programming constraints.

System of Linear Programming:

z=−3x+5y

x+y≥−22

x−y≥−4

x−y≤2

Minimum value of z:

Answer 1

The minimum value of z is -38

How to identify the vertices of the feasible region for the given linear programming constraints?

The optimization equation is given as

z=−3x+5y

The constraints are given as:

x+y≥−2

3x−y≤2

x−y≥−4

Next, we plot the constraints on a graph and determine the points of intersections

See attachment for the graph

From the attached graph, the points of intersections are

(-9, -13) and (-10, -12)

So, we have:

(-9, -13)

(-10, -12)

Substitute these values in the objective function

z=−3x+5y

This gives

z= −3 * -9 +5 * -13 = -38

z= −3 * -10 +5 * -12 = -30

-38 is less than -30

Hence, the minimum value of z is -38

So, the complete parameters are:

Optimization Equation:

z=−3x+5y

Constraints:

x+y≥−2

3x−y≤2

x−y≥−4

Vertices of the feasible region

(0, -2)

(-3, 1)

(3, 7)

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