Explanation Given Information: The provided inequalities are − 3 x + 2 y ≤ 5 , 3 x − 2 y ≤ 6 , x ≤ 2 y , x ≥ 0 and y ≥ 0 Graph: Consider the provided inequalities are, − 3 x + 2 y ≤ 5 , 3 x − 2 y ≤ 6 , x ≤ 2 y , x ≥ 0 and y ≥ 0 , Consider the inequality − 3 x + 2 y ≤ 5 Assume the equation as, − 3 x + 2 y = 5 Now, substitute the values of x in order to get the corresponding values of y and sketch the graph of the line. For x = 0 − 3 ( 0 ) + 2 y = 5 2 y = 5 y = 5 2 Therefore, the point is ( 0 , 5 2 ) For x = − 5 3 − 3 ( − 5 3 ) + 2 y = 5 2 y = 0 y = 0 Therefore, the point is ( − 5 3 , 0 ) For x = 1 − 3 ( 1 ) + 2 y = 5 2 y = 8 y = 4 Therefore, the point is ( 1 , 4 ) . The points for the equation − 3 x + 2 y = 5 are as follows: x y ( x , y ) 0 5 2 ( 0 , 5 2 ) − 5 3 0 ( − 5 3 , 0 ) 1 4 ( 1 , 4 ) The graph of the inequality is as follows: Hence, the boundary points for the equation are ( − 1.66 , 0 ) and ( 0 , 2.5 ) . Consider the inequality, 3 x − 2 y ≤ 6 Assume the equation as, 3 x − 2 y = 6 Now, substitute the values of x in order to get the corresponding values of y and sketch the graph of the line. For x = 0 3 ( 0 ) − 2 y = 6 − 2 y = 6 y = − 3 Therefore, the point is ( 0 , − 3 ) . For x = 2 3 ( 2 ) − 2 y = 6 − 2 y = 0 y = 0 Therefore, the point is ( 2 , 0 ) . For x = 1 , 3 ( 1 ) − 2 y = 6 − 2 y = 3 y = − 3 2 Therefore, the point is ( 1 , − 3 2 ) . The points for the equation 3 x − 2 y = 6 are as follows: x y ( x , y ) 0 − 3 ( 0 , − 3 ) 2 0 ( 2 , 0 ) 1 − 3 2 ( 1 , − 3 2 ) The graph of the inequality is as follows:

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.1, Problem 23E

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To graph: The inequalities −3x+2y≤5, 3x−2y≤6, x≤2y, x≥0 and y≥0 and also check whether the region of the inequalities are bounded or unbounded and find the coordinates of all the corner points if possible.

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Chapter 5.1, Problem 22E

Chapter 5.1, Problem 24E

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To graph: The inequalities − 3 x + 2 y ≤ 5 , 3 x − 2 y ≤ 6 , x ≤ 2 y , x ≥ 0 and y ≥ 0 and also check whether the region of the inequalities are bounded or unbounded and find the coordinates of all the corner points if possible.

Solution Summary: The author analyzes the inequality -3x+2yle 5,3x-2y

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To graph: The inequalities −3x+2y≤5, 3x−2y≤6, x≤2y, x≥0 and y≥0 and also check whether the region of the inequalities are bounded or unbounded and find the coordinates of all the corner points if possible.

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Chapter 5 Solutions