minimum and maximum of the function 2HELP!!!

Find the minimum and maximum of the function f=3x+2y subject to
y is less than/equal to 6
x is greater than/equal to 3
3x+6y greater than/equal to 27
Type N if the answer does not exist. minimum is and maximum is .

Comments for minimum and maximum of the function 2HELP!!!

 Apr 18, 2011 Minimum and Maximum of Objective Function by: Staff The question: Find the minimum and maximum of the function f=3x+2y subject to y is less than/equal to 6 x is greater than/equal to 3 3x+6y greater than/equal to 27 Type N if the answer does not exist. minimum is and maximum is . The answer: Find the minimum and maximum of the function f=3x+2y subject to y ≤ 6 x ≥ 3 3x + 6y ≥ 27 When these boundaries are plotted, they form the Unbounded Feasible Region (click link to view, use the Backspace key to return to this page): http://www.solving-math-problems.com/images/min-max-function-20110417-2a-feasible-region.png Corner points: The corner points are shown in the following graph (click link to view, use the Backspace key to return to this page): http://www.solving-math-problems.com/images/min-max-function-20110417-2b-corner-points.png There are only two extreme corners The intersection of x = 3 and y = 6: (3 ,6) The intersection of x = 3 and 3x + 6y = 27: (3 ,3) (3 ,6), (3 ,3) Value of f(x,y) = 3x + 2y at corners f(x,y) = 3x + 2y f(x,y) = 3*3 + 2*6 = 21 f(x,y) = 3*3 + 2*3 = 15, minimum value of f A maximum value cannot be determined since the value of x can grow infinitely. Minimum value of f is: 15; when x = 3 and y = 3 Thanks for writing. Staff www.solving-math-problems.com