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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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) = ( , , )
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:
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:
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