Explanation Given Information: The provided function g = 22 x + 17 y subject to 8 x + 5 y ≥ 100 , 12 x + 25 y ≥ 360 , x ≥ 0 and y ≥ 0 . Formula used: The following procedure used to solve linear programming problem with graphical method. The following method is used, Step 1. Write the function from the problem. Step-2 Plot the solution of the system of equation. Step 3. Check if the region is closed or not. Step 4 If the region is not bounded by constrain equation, check whether an optimal value exits. If not, state this. If so, go to step 5. Step 5. Find the corners of the feasible region. Step 6. Calculate the function value at each corner of the feasible region. Step 7. Find the maximum or minimum value of the function. Calculation: Consider the given function g = 22 x + 17 y subject to 8 x + 5 y ≥ 100 , 12 x + 25 y ≥ 360 , x ≥ 0 and y ≥ 0 . Graph the solution of given constraint 8 x + 5 y ≥ 100 , 12 x + 25 y ≥ 360 , x ≥ 0 and y ≥ 0 can be draw by calculating its cooridante. The following table show the coordinates of constraint 8 x + 5 y ≥ 100 x -coordinate y -coordinate 8 x + 5 y ≥ 100 The coordinates ( x , y ) 12.5 0 ( 12.5 , 0 ) 0 20 ( 0 , 20 ) The following table show the coordinates of constraint 12 x + 25 y ≥ 360 x -coordinate y -coordinate 12 x + 25 y ≥ 360 The coordinates ( x , y ) 30 0 ( 30 , 0 ) 0 14.4 ( 0 , 14.4 ) The intersection of 8 x + 5 y = 100 and 12 x + 25 y = 360 will be, Substitute 360 − 12 x 25 for y in 8 x + 5 y = 100 , 8 x + 5 y = 100 8 x + 5 ( 360 − 12 x 25 ) = 100 8 x + 1800 − 60 x 25 = 100 Solve further, 200 x + 1800 − 60 x 25 = 100 140 x = 2500 − 1800 x = 5 Substitute 5 for x in 8 x + 5 y = 100

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 4.2, Problem 18E

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To calculate: The minimize value of function g=22x+17y subject to 8x+5y≥100,12x+25y≥360, x≥0 and y≥0.

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Chapter 4.2, Problem 17E

Chapter 4.2, Problem 19E

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The minimize value of function g = 22 x + 17 y subject to 8 x + 5 y ≥ 100 , 12 x + 25 y ≥ 360 , x ≥ 0 and y ≥ 0 .

Solution Summary: The author explains the procedure used to solve linear programming problem with graphical method.

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To calculate: The minimize value of function g=22x+17y subject to 8x+5y≥100,12x+25y≥360, x≥0 and y≥0.

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