Explanation Given Information: The provided function is C = x + 3 y subjected to x + 4 y ≤ 12 , y ≤ 2 , x + y ≤ 9 , x ≥ 0 and y ≥ 0 . Formula used: The following procedure used to solve linear programming problem with graphical method. Step-1. Now write the objective function and constrain inequality from the provided problem. Step-2. Now graph the solution of the constraint system. If the feasible region is closed and bounded proceed to step 3. If the region is not closed and constrained, check whether an ideal value exits. If not, state this. If so, proceed to step 3. Step-3. Evaluate the corners of the resulting feasible region. This may require simultaneous solution of two or more pairs of boundary equations. Step-4. Evaluate the objective function at each corner of the feasible region determine by constraint Step-5. If two-corner give the ideal value of the objective function, then all points on the boundary line joining these two corner also optimize the function. Calculation: Consider the provided constrained, x + 4 y ≤ 12 , y ≤ 2 , x + y ≤ 9 Now consider the first constrained, x + 4 y ≤ 12 Assume the constrioned in the equation form as shown below, x + 4 y = 12 Substitute y = 0 into the equation x + 4 y = 12 , x + 4 ( 0 ) = 12 x = 12 Substitute x = 0 into the equation x + 4 y = 12 , 0 + 4 y = 12 4 y = 12 y = 12 3 y = 4 The following table show the coordinates of constraint x + 4 y ≤ 12 x -coordinate y -coordinate x + 4 y ≤ 12 The coordinates ( x , y ) 12 0 ( 12 , 0 ) 0 4 ( 0 , 4 ) Now consider the second constrained, x + y ≤ 9 Assume the constrioned in the equation form as shown below, x + y = 9 Substitute y = 0 into the equation x + y = 9 , x + 0 = 9 x = 9 Substitute x = 0 into the equation x + y = 9 , 0 + y = 9 y = 9 The following table show the coordinates of constraint x + y ≤ 9 x -coordinate y -coordinate x + y ≤ 9 The coordinates ( x , y ) 9 0 ( 9 , 0 ) 0 9 ( 0 , 9 ) The intersection of x + 4 y = 12 and x + y = 9 will be, Substitute 9 − x for y in the equation x + 4 y = 12 as below, x + 4 y = 12 x + 4 ( 9 − x ) = 12 x + 36 − 4 x = 12 x = 8 Substitute 8 for x in the equation x + 4 y = 12 as below, x + 4 y = 12 8 + 4 y = 12 y = 1 The intersection of x + 4 y = 12 and x + y = 9 will be ( 8 , 1 )

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 14E

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To calculate: The maximum value of function C=x+3y subjected to

x+4y≤12,y≤2,x+y≤9, x≥0 and y≥0.

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Chapter 4.2, Problem 13E

Chapter 4.2, Problem 15E

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The maximum value of function C = x + 3 y subjected to x + 4 y ≤ 12 , y ≤ 2 , x + y ≤ 9 , x ≥ 0 and y ≥ 0 .

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

Videos

To calculate: The maximum value of function C=x+3y subjected to

x+4y≤12,y≤2,x+y≤9, x≥0 and y≥0.

Want to see the full answer?

Chapter 4 Solutions

The maximum value of function C = x + 3 y subjected to x + 4 y ≤ 12 , y ≤ 2 , x + y ≤ 9 , x ≥ 0 and y ≥ 0 .

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

Videos

To calculate: The maximum value of function C=x+3y subjected to x+4y≤12,y≤2,x+y≤9, x≥0 and y≥0.

Want to see the full answer?

Chapter 4 Solutions

To calculate: The maximum value of function C=x+3y subjected to

x+4y≤12,y≤2,x+y≤9, x≥0 and y≥0.