The statement if the constraint region of linear programming lays in quadrant I and is unbounded, the objective function cannot have the maximum value is true or false.
Answer to Problem 49E
The given statement is true that the objective function have the maximum value.
Explanation of Solution
Given:
The constraint region of linear programming lays in quadrant I and is unbounded, the objective function cannot have the maximum value is true or false.
Formula used:
The substitution method is used.
Calculation:
Consider that a linear programming problem has maximum value at two vertices.
Consider the objective function is,
Where,
In such case the objective function has infinitely many solutions. These solutions will appear on the line joining the two vertices with the maximum value.
In the above plot the maximum value occurs at two points on that line. The value of x and yon that line varies proportionally so that the optimal value remains the same.
Thus, the given statement is true that the objective function have the maximum value.
Conclusion:
The given statement is true that the objective function have the maximum value
Chapter 7 Solutions
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