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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 .

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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

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