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April 21, 2014

Homework Help: PLEASE HELP... ALGEBRA.... LINEAR PROGRAMMING

Posted by Anonymous on Wednesday, October 11, 2006 at 10:06am.

HELP ME WITH THESE 2 PROBLEMS PLEASE.....

1. Objective Quantity: C= 5x+4y
Constraints:
x < -2
x > -4
y > 1
y < 6
All of the signs have lines under them.

2. Objective Quantity: C= 6x + 2y
Constraints:
x > 0
x < 5
y > 0
4x-y > 1
Again, all of the signs have lines under them.


You have to plot the areas enclosed by these constraints. Take the second one, for instance.
Objective Quantity: C= 6x + 2y
Constraints:
x >= 0
x <= 5
y >= 0
4x-y >= 1

change the last to y<=4x-1

Test the corners on the graph with the Cost function (objective function). You did not say whether you are maximizing, or minimizing the C function. Choose the corner (max, min) that you need.

Summary: Graph the lines, which will enclose an area. Test the corners with the objective function. THe solution will lie on one corner.


As BobP said, e need to know if you're trying to maximize or minimize the the objective quantity.
For the first one there are two sets of parallel lines, so the vertices where the lines intersect need to be checked. They are
(-4,1),(-4,6),(-2,1),(-2,6)
For the second one, we're interested in solutions in the first quadrant and are on the lines x=5 and 4x-y=>1. The constraints form a triangle, which you should verify.
The vertices are
(1/4,0),(5,0),(5,19)

Yes

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