Question:
Minimize z = 2x + 6y
Subject to
2x + y >= 2;
3x + 4y <= 12
x,y >=0
Is min z = 2 the right answer ? if not how do i solve this ?
[Math] Minimize LPP using graphical method [ operational research ]
linear programmingoperations research
linear programmingoperations research
Question:
Minimize z = 2x + 6y
Subject to
2x + y >= 2;
3x + 4y <= 12
x,y >=0
Is min z = 2 the right answer ? if not how do i solve this ?
Best Answer
\begin{align} \min_{x,y}\quad & 2x+6y \\2x +y &\geq 2 \\3x+4y&\leq 12 \\x,y &\geq0 \end{align} The easiest way to solve this graphically would be to list down the corner points and the value of the objective function at each.
If you do that, you can see that $(1,0)$ has the lowest objective value of $2$ (As you pointed out). And since the optimal solution of a Linear Programming Problem always lies on the corner points, this is the global optimum of the problem.