Given the LP problem
I know that the dual will be
I know that the optimal value of the LP problem is 7.5 and that the values of x1 and x2 are respectively (0.5,3).
However I am not sure how to solve the values of the dual problem since there are three variables.
On the LP problem i found the solutions by the graphical method and equated the first constraint to the second constraint.
I am not sure I can do this with the dual since there are three variables. I have some learning disabilities and If you may explain how to get to y1,y2,y3 in the simplest way possible it would be greatly appreciated.
On the answer sheet it states that the optimal of the dual is (7/4, 1/4 and 0).
Guide:
The third constraint in the primal is not active, hence the corresponding dual variable, $y_3$ must take value $0$ by complementary slackness condition.
Now having $y_3$ fixed to be $0$. It is now a $2$-variable LP and you can solve for $y_1$ and $y_2$.