SOLUTION: Consider the following simplex tableau. x y u v P Constants 1 1 1 0 0 1 1 0 −1 1 0 5 5 0 7 0 1 18 Since the simplex tableau is in final form, write the optimal solu

Algebra ->  College  -> Linear Algebra -> SOLUTION: Consider the following simplex tableau. x y u v P Constants 1 1 1 0 0 1 1 0 −1 1 0 5 5 0 7 0 1 18 Since the simplex tableau is in final form, write the optimal solu      Log On


   

Question 1202912: Consider the following simplex tableau.
x y u v P Constants
1 1 1 0 0 1
1 0 −1 1 0 5
5 0 7 0 1 18

Since the simplex tableau is in final form, write the optimal solution and the optimal value.
Optimal Solution:
(x,y) =

Optimal Value:
P =18
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!


Change to a system of equations:

system%281x%2B1y%2B1u%2B0v%2B0P=1%2C+1x%2B0y-1u%2B1v%2B0P=5%2C5x%2B0y%2B7u%2B0v%2B1P=18%29

Simplify:
system%28x%2By%2Bu=1%2C+x-u%2Bv=5%2C5x%2B7u%2BP=18%29

All of the variables are non-negative.  Solve the last equation for P:

P=18-5x-7u

To make P large as possible choose what is subtracted from it to be 0,
so we can keep the whole 18 for P if we choose x = 0 and u = 0.
Substituting:

system%280%2By%2B0=1%2C+0-0%2Bv=5%2C5%280%29%2B7%280%29%2BP=18%29

system%28y=1%2Cv=5%2CP=18%29

Choose x = 0, y = 1, for a maximum value of P = 18.

Edwin