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| PAGE: 411 | SET: Exercises | PROBLEM: 19 |
The constraints are
The objective function is 
.
Graph :
Graph the inequalities and shade the required region.
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Note : The shaded region is the set of solution points for the objective function.
Observe the graph,
Tabulate the solutions of each of two system of inequalities and obtain the intersection points.
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System of boundary equations |
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| Solution (vertex points) |  |
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Find the value of objective function at the solution points.
At point , 
.
At point , 
.
At point , 
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The object function have many solutions for different values of 
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Let 
.
Substituite 
in maximum and minimum values.
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Observe the values of 
,
The maximum value of 
is 
when 
and 
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The minimum value of is
when 
and .
The maximum at point is 
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The minimum at point is 
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