To calculate: The coordinates of the vertices of the feasible region formed by graphing the given inequalities
Answer to Problem 3CYU
The graph of the given system of inequalities is,
The coordinates of the feasible region are
The maximum value of the function is either unknown or does not exist and minimum value of the function is
Explanation of Solution
Given information:
The inequalities
Formula used:
Linear programming is a technique to find the maximum and the minimum value of a given function over a given system of some inequalities, with each inequality representing a constraint. Graph the inequalities and obtain the vertices of the feasible region (solution set). Substitute the coordinates of the feasible region in the function and determine the maximum and the minimum value.
Calculation:
Consider the provided system of inequalities
Recall that linear programming is a technique to find the maximum and the minimum value of a given function over a given system of some inequalities, with each inequality representing a constraint. Graph the inequalities and obtain the vertices of the feasible region (solution set).
Graph the given inequalities and locate the vertices of the feasible region.
Since, it is an unbounded region, the vertices of the region cannot be accurately determined. There can be infinite many points in this unbounded region, so, take the corner points where the system of inequalities cut each other,
Now, to find the maximum and minimum value of the function, substitute the coordinates of the feasible region in the function and determine the maximum and the minimum value.
So, substitute
From the above table, it is observed that the minimum value of the function is
The maximum value of function is unknown or does not exist because there are infinite many points in the unbounded region which can give different maximum values at different points. So, the maximum value of function is either unknown or does not exist.
Thus, graph of the given system of inequalities is,
The coordinates of the feasible region are
Chapter 3 Solutions
Algebra 2
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