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Algebra II Linear Programming

by Michelle
(Spartanburg, SC)











































what is the minimum value of 4x + 3y in the feasible region?

Comments for Algebra II Linear Programming

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May 09, 2011
Minimum Value of 4x + 3y
by: Staff

The question:

by Michelle
(Spartanburg, SC)

what is the minimum value of 4x + 3y in the feasible region?

The answer:

The objective function is:

f(x,y) = 4x + 3y

The minimum value of 4x + 3y depends upon the feasible region.

You did not specify what the constraints should be placed on this function, so I'm going to assume the feasible region is:

x ≥ 0

y ≥ 0


When this is taken into account, your question becomes:

Find the minimum of the objective function f(x,y) = 4x + 3y

subject to

x ≥ 0

y ≥ 0


When these boundaries are plotted, they form an UNBOUNDED FEASIBLE REGION.

(1) Click the following link to VIEW this GRAPH; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:


http://www.solving-math-problems.com/images/unbounded-feasible-region-01.png



The objective function f(x,y) = 4x + 3y can be plotted on the same graph.

f(x,y) = 4x + 3y has a slope of -4/3

To find the minimum value of f(x,y), look at the corner point f(0,0):

f(0,0) = 4*0 + 3*0

f(0,0) = 0

When 0 = 4x + 3y is plotted, the curve passes through the origin (which is the only corner point).

(1) Click the following link to VIEW this GRAPH; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/4x-plus-3y-min-value.png


the final answer is:

Minimum value of 4x + 3y is: 0; when x = 0 and y = 0


Thanks for writing.

Staff
www.solving-math-problems.com


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