Explanation Given Information: Maximize the function p = x y subject to x ≥ 0 , y ≥ 0 , x + y ≤ 2 . Formula Used: Graphical method to solve the linear programing of the function. Step1: Draw the graph of the constraint of the region. Step2: Calculate the value of corner point. Step3: To find the optimum value of the function substitute the corner point in the objective function to see the point at which gives the maximum value. Step4: Any corner point gives the optimum value. Calculate: Consider the provided constraint, x ≥ 0 , y ≥ 0 , x + y ≤ 2 Draw the graph of the all constraint in same coordinate system, Here the corner point of the constraint is ( 0 , 0 ) , ( 2 , 0 ) , ( 0 , 2 ) . So, check the maximization of the function at the corner point that is given in the table, Point Line through the point Coordinate p = x y A ( 0 , 0 ) 0 B ( 2 , 0 ) 0 C ( 0 , 2 ) 0 From the above table, it is concluded that all corner points the value of function is zero

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.2, Problem 65E

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To prove: The value of p is zero on every corner point but is greater than zero at many non- zero at many non-corner point if p=xy subject to x≥0, y≥0 and x+y≤2.

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Chapter 5.2, Problem 64E

Chapter 5.2, Problem 66E

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To prove: The value of p is zero on every corner point but is greater than zero at many non- zero at many non-corner point if p = x y subject to x ≥ 0 , y ≥ 0 and x + y ≤ 2 .

Solution Summary: The author concludes that the value of p is zero on every corner point but is greater than zero at many non- zero points.

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To prove: The value of p is zero on every corner point but is greater than zero at many non- zero at many non-corner point if p=xy subject to x≥0, y≥0 and x+y≤2.

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Chapter 5 Solutions