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Consider following optimization problem

Maximize$\ \ \ \ \ \ \ \ -x_1+x_2$

subjected to $\ \ \ \ \ \ \ 3x_1+4x_2=12$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x_1-x_2\leq12$

$x_1,x_2\geq0$

It is given that start with initial basic feasible solution $(x_1,x_2)$=(4,0)

My question is now how to proceed further to solve the problem.

Abhinav Sharma
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    Are you familiar with the simplex algorithm? If not, try a graphical approach, it should be fairly easy here in 2d. – Kuifje Aug 04 '16 at 20:14
  • A supplementary hint: the "feasibility polygon" is here very thin... Show efforts : if not, we will think that you want us to do your homework. – Jean Marie Aug 04 '16 at 20:50
  • @Moo- yes the problem is correct. – Abhinav Sharma Aug 05 '16 at 11:40
  • @JeanMarie : I plotted the feasible region and yes it is very thin. It is a straight line connecting (4,0) and (0,3). What I need to know is that if initial basic solution is given for a problem, then how to proceed. Because normally we add slack variable to each equation and put these slack variables in basis. Now here I have initial basic solution in terms of x1 and x2. Now how to do the next iteration. – Abhinav Sharma Aug 05 '16 at 11:43
  • The maximum is reached with $(x_1,x_2)=(0,3)$ with value $3$, because, by moving up along the line segment joining $(0,4)$ to $(3,0)$ you always increase $x_2$ while decreasing $x_1$. Thus the economical function $x_2-x_1$ always increases. As you cannot go further than point $(3,0)$, you have thus reached the maximum – Jean Marie Aug 05 '16 at 21:43

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