minimum and maximum of the function HELP!!!
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minimum and maximum of the function HELP!!!

Find the minimum and maximum of the function f=4x−4y subject to
y is greater than/equal to 4
y is less than/equal to 8
4x−3y is greater than/equal to -12
4x+y is less than/equal to 44
Type N if the answer does not exist. minimum is and maximum is .

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minimum and maximum of the function HELP!!!

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Apr 18, 2011
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starstarstarstarstar 		Minimum and Maximum of Objective Function
by: Staff


The question:

Find the minimum and maximum of the function f=4x−4y subject to

y is greater than/equal to 4
y is less than/equal to 8
4x−3y is greater than/equal to -12
4x+y is less than/equal to 44
Type N if the answer does not exist. minimum is and maximum is .


The answer:

Find the minimum and maximum of the function f=4x−4y

subject to

y ≥ 4
y ≤ 8
4x - 3y ≥ -12
4x + y ≤ 44


When these boundaries are plotted, they form the Bounded 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-20110417-1a-feasible-region.png

The bounded feasible region (shown as the yellow shaded area) defines a maximum value and a minimum value for the objective function (f = 4x - 4y).

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-20110417-1b-corner-points.png


The four corner points are:

The intersection of 4x - 3y = -12 and y = 4: (0 ,4)

The intersection of 4x - 3y = -12 and y = 8: (3 ,8)

The intersection of 4x + y = 44 and y = 8: (9 ,8)

The intersection of 4x + y = 44 and y = 4: (10 ,4)


(0, 4), (3, 8), (9, 8), (10, 4)


Find the maximum and minimum values of f = 4x - 4y.

f = 4x - 4y

f = 4*0 – 4*4 = -16

f = 4*3 - 4*8 = -20, minimum value of f

f = 4*9 - 4*8 = 4

f = 4*10 - 4*4 = 24, maximum value of f


Maximum value of f is: 24; when x = 10 and y = 4
Minimum value of f is: -20; when x = 3 and y = 8

Thanks for writing.


Staff
www.solving-math-problems.com


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