solving a linear programming problem

Såxon · #1 $Old$ March 29th, 2009, 01:41 PM

Solve the linear programming problem. Maximize C = -3x +5y subject to:
x - y greater than or equal to -3
2x + y less than or equal to 12
x greater than or equal to 0
y greater than or equal to 0

For the x intercept i got (6,0) and the y i got (0,3) the point of interception of the 2 equations x-y=-3 and 2x+y=12 i got (3,6)

can someone show me where to go from here?
what does the maximize C = -3x + 5y even mean?

SENTINEL4 · #2 $Old$ March 29th, 2009, 03:15 PM

Hey there...
I don't know exactly what you have to do...
I had a lesson "Linear programming" last year and i think that the first step is to solve it graphically according to your restrictions.
It depends what the exercise wants you to do.
The max c=..... means that you have to find which x and y according to destrictions below gives you the max price of c.

P.S. Excuse me for my english if i have any errors...

chisigma · #3 $Old$ March 29th, 2009, 03:33 PM

In general the solution that maximizes [or minimizes] a linear function of a set o variables $x_{1},x_{2},\dots$ is one of the 'estreme admissible points', that means one of the 'vertex' that are compatible with the constrains. Here we are in two dimension and the problem is easy enough...

The 'extreme admissible points' are $A(0,0),B(0,3),C(3,6),D(6,0)$ . A simple check verifies that the quantity $c=-3\cdot x + 5 \cdot y$ has its maximum in C, where the value is $c= 21$ ...

Kind regards

stapel · #4 $Old$ March 29th, 2009, 03:34 PM

Quote:

Originally Posted by Såxon $View Post$

can someone show me where to go from here?
what does the maximize C = -3x + 5y even mean?

Plug the corner points into the "max/min" equation (in your case, a "max" equation). Whichever point gives you the largest value is your solution.

For a complete explanation, try here.