SOLUTION: Consider the following final tableau corresponding to a linear programming problem. x y z u v w P Constants 0 0 −1/2 1 −1/4 −1/4

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Question 1202966: Consider the following final tableau corresponding to a linear programming problem.
x y z u v w P Constants
0 0 −1/2 1 −1/4 −1/4 0 2
0 1 0 0 1/4 −1/4 0 3
1 0 3/2 0 0 1/2 0 15
0 0 1 0 3/2 1/2 1 78
Part 1 of 2
(a.) How many solutions does the linear programming problem have?
One Solution
Part 2 of 2
(b.) Since the linear programming problem has one solution, provide the solution as a point.
(x, y, z) = ( , , )
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
How did you know there was only 1 solution if you didn't know how to do
the other part?  Did you just guess?



That is the matrix for this system of equations:



Solve the bottom equation for P:

P=78-z-expr%283%2F2%29v-expr%281%2F2%29w

We want P to be as large as possible, and we have three non-negative numbers
subtracted from the 78.  We can keep the whole 78 for P by choosing all three
variables z, v, and w = 0.  So we substitute those in the system and get:

system%28u=2%2C%0D%0Ay+=+3%2C%0D%0Ax+=+15%2C%0D%0AP=78%29

So P has a maximum value of 78 when x = 15, y = 3, and z = 0.  The point is

(x,y,z) = (15,3,0)

Edwin