Explanation Given Information: The provided inequalities are 30 x + 20 y ≥ 600 , 10 x + 40 y ≥ 400 , 20 x + 30 y ≥ 600 , x ≥ 0 and y ≥ 0 Graph: Consider the provided inequalities are, 30 x + 20 y ≥ 600 , 10 x + 40 y ≥ 400 , 20 x + 30 y ≥ 600 , x ≥ 0 and y ≥ 0 , Consider the inequality 30 x + 20 y ≥ 600 Assume the equation as, 30 x + 20 y = 600 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 30 ( 0 ) + 20 y = 600 20 y = 600 y = 30 Therefore, the point is ( 0 , 30 ) For x = 20 30 ( 20 ) + 20 y = 600 20 y = 0 y = 0 Therefore, the point is ( 20 , 0 ) For x = 1 , 30 ( 1 ) + 20 y = 600 20 y = 570 y = 57 2 Therefore, the point is ( 1 , 57 2 ) The points for the equation 30 x + 20 y = 600 are as follows: x y ( x , y ) 0 30 ( 0 , 30 ) 5 0 ( 20 , 0 ) 1 57 2 ( 1 , 57 2 ) The graph of the inequality is as follows: Hence, the boundary points for the equation are ( 20 , 0 ) and ( 0 , 30 ) . Consider the inequality 10 x + 40 y ≥ 400 Assume the equation as, 10 x + 40 y = 400 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 , 10 ( 0 ) + 40 y = 400 40 y = 400 y = 10 Therefore, the point is ( 0 , 10 ) , For x = 40 , 10 ( 40 ) + 40 y = 400 40 y = 0 y = 0 Therefore, the point is ( 40 , 0 ) , For x = 1 , 10 ( 1 ) + 40 y = 400 40 y = 390 y = 39 4 Therefore, the point is ( 1 , 39 4 ) The points for the equation 10 x + 40 y = 400 are as follows: x y ( x , y ) 0 10 ( 0 , 10 ) 40 0 ( 40 , 0 ) 1 39 4 ( 1 , 39 4 ) . The graph of the inequality is as follows: Hence, the boundary points for the equation are ( 40 , 0 ) and ( 0 , 10 ) . Consider the inequality 20 x + 30 y ≥ 600 Assume the equation as, 20 x + 30 y = 600 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 , 20 ( 0 ) + 30 y = 600 30 y = 600 y = 20 Therefore, the point is ( 0 , 20 ) . For x = 30 , 20 ( 30 ) + 30 y = 600 30 y = 0 y = 0 Therefore, the point is ( 30 , 0 ) . For x = 1 , 20 ( 1 ) + 30 y = 600 30 y = 580 y = 58 3 Therefore, the point is ( 1 , 58 3 ) The points for the equation 20 x + 30 y = 600 are as follows: x y ( x , y ) 0 20 ( 0 , 20 ) 30 0 ( 30 , 0 ) 1 58 3 ( 1 , 58 3 )

7th Edition

ISBN: 9781337291262

Author: Stefan Waner, Steven Costenoble

Publisher: Brooks Cole

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Chapter 5.1, Problem 22E

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To graph: The inequalities 30x+20y≥600, 10x+40y≥400, 20x+30y≥600, 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 21E

Chapter 5.1, Problem 23E

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To graph: The inequalities 30 x + 20 y ≥ 600 , 10 x + 40 y ≥ 400 , 20 x + 30 y ≥ 600 , 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 explains how to graph the inequalities of 30x+20yge 600,

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To graph: The inequalities 30x+20y≥600, 10x+40y≥400, 20x+30y≥600, 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