Question 1202965: Consider the following final tableau corresponding to a linear programming problem.
x y u v w P Constants
0 0 1 −23/5 12/5 0 48
0 1 0 3/5 −2/5 0 6
1 0 0 −2/5 3/5 0 21
0 0 0 0 5 1 375
Part 1 of 2
(a.) How many solutions does the linear programming problem have?
Infinite Solutions
Part 2 of 2
(b.) Since the linear programming problem has infinitely many solutions, describe the line segment containing the solutions by providing two points. (Enter the point with the smaller x-value first.)
There are infinitely many solutions on the line segment connected by the points
(21, 6) "this is correct"
and
( , ) "I need help on the last point"
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
How did you know there was infinitely many solutions? I don't know how to tell
until I do the other part.
x y u v w P Constants
0 0 1 −23/5 12/5 0 48
0 1 0 3/5 −2/5 0 6
1 0 0 −2/5 3/5 0 21
0 0 0 0 5 1 375
That is the matrix for this system of equations:
Solve the bottom equation for P:
We want P to be as large as possible, and we have one non-negative number
subtracted from the 375. We can keep the whole 375 for P by choosing the
variable v = 0. So we substitute v = 0 in the system and get:
So P has a maximum value of 375.
So since x and y depend on v and since there are infinitely many values
we can choose for v, there are infinitely many solutions.
If we choose v=0, we get the point (x,y) = (21,6) on the line, which you have.
To get another point on the line, to make it a whole number, choose a multiple
of 5, say 5, and get (x,y) = (23,3).
If you wanted a third point, choose another multiple of 5, say 10, and get
(x,y) = (25,0).
Edwin
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