Explanation Given Information: The given function is, g = x + 5 y And the given inequalities are, 8 x + y ≥ 85 x + y ≥ 50 x + 4 y ≥ 80 x + 10 y ≥ 104 Restrict x ≥ 0 , y ≥ 0 . Formula used: The following method is used, Step 1. Write the function from the problem. Step 2. Check if the region is closed or not. Step 3. Find the corners of the feasible region. Step 4. Evaluate the function at each corner of the feasible region. Step 5. Find the maximum value of the function. Calculation: Consider the given function and inequalities, g = x + 5 y Subject to: 8 x + y ≥ 85 x + y ≥ 50 x + 4 y ≥ 80 x + 10 y ≥ 104 Restrict x ≥ 0 , y ≥ 0 . The two inequalities x ≥ 0 , y ≥ 0 restrict the solution to first quadrant. To graph theses inequalities, first draw the graph for the following four lines as a solid line because points lying on the line satisfy the given inequalities, 8 x + y = 85 ......(1) x + y = 50 ......(2) x + 4 y = 80 ......(3) x + 10 y = 104 ......(4) So, solve the first equation for y , 8 x + y = 85 y = 85 − 8 x Now, find three solutions for this equation as, x y = 85 − 8 x y 0 85 − 8 ( 0 ) = 85 − 0 85 5 85 − 8 ( 5 ) = 85 − 40 45 10 85 − 8 ( 10 ) = 85 − 80 5 The solution for the first equation are ( 0 , 85 ) , ( 5 , 45 ) , ( 10 , 5 ) . Now solve the second equation for y , x + y = 50 y = 50 − x Now, find three solutions for this equation as, x y = 50 − x y 0 50 − ( 0 ) 50 20 50 − ( 20 ) 30 50 50 − ( 50 ) 0 The solution for the first equation are ( 0 , 50 ) , ( 20 , 30 ) , ( 50 , 0 ) . Now solve the third equation for y , x + 4 y = 80 4 y = 80 − x y = 80 − x 4 Now, find three solutions for this equation as, x y = 80 − x 4 y 0 80 − ( 0 ) 4 = 80 4 20 40 80 − ( 40 ) 4 = 40 4 10 80 80 − ( 80 ) 4 = 0 4 0 The solution for the third equation are ( 0 , 20 ) , ( 40 , 10 ) , ( 80 , 0 )

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 4, Problem 13RE

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To calculate: The minimize value of function g=5x+3y that subjected to constrains 8x+y≥85,x+y≥50,x+4y≥80,x+10y≥104, x≥0 and y≥0.

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Chapter 4, Problem 12RE

Chapter 4, Problem 14RE

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Mathematical Applications for the Management, Life, and Social Sciences

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The minimize value of function g = 5 x + 3 y that subjected to constrains 8 x + y ≥ 85 , x + y ≥ 50 , x + 4 y ≥ 80 , x + 10 y ≥ 104 , x ≥ 0 and y ≥ 0 .

Solution Summary: The author explains the formula used to calculate the minimize value of function g=5x+3y that subjected to constraints.

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To calculate: The minimize value of function g=5x+3y that subjected to constrains 8x+y≥85,x+y≥50,x+4y≥80,x+10y≥104, x≥0 and y≥0.

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Chapter 4 Solutions