Question

Instructions: Identify the vertices of the feasible region for the given linear programming constraints.

Optimization Equation:
z=−3x+5y

Constraints:
x+y≥−2
3x−y≤2
x−y≥−4

Fill in the vertices of the feasible region:

(0, )
(−3, )
(3, )

Answer 1

The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

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

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

So, we have:

(0, -2)

(-3, 1)

(3, 7)

Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

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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