Question

Whether the statement "I need to be able to graph systems of linear inequalities in order to solve linear programming problems" makes sense or not.

Alternate coordinate systems
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asked 2020-11-08
Whether the statement "I need to be able to graph systems of linear inequalities in order to solve linear programming problems" makes sense or not.

Answers (1)

2020-11-09
Let \(\displaystyle{z}={a}{x}\ +{b}{y}\) be an objective function that depends on x and y. Also, z is subject to a number of constraints on x and y. If a maximum or minimum value of z exist, the linear programming problem can be solved as follows:
Step1: Graph the system of inequalities that represents the constraints.
Step 2: Obtain the value of the objective function at each corner of the graphed region.
The maximum and ninimum of the objective function will occur at one or more corner points.
Thus, to find the maximum or minimum values of a linear programming problem, the coordinates of each vertex from the graph representing the constraints need to be substituted in the objective function.
Hence, the given statement makes sense.
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