Suppose that P and Q are two of the corner points of the feasible region lying completely in the first quadrant. In addition, P is located at South-East of Q*.
z = 0 (or more specifically, Ax + By = 0) is a profit function (or any other terms applicable) with positive slope.
To find graphically at which corner point that max(z) is obtained is by drawing lines L1, L2, …, Ln, parallel to z = 0 towards the SE direction*. This way, we found Ln hits P.
Judging from the method used above, we can reasonably re-phrase the above by just finding which of the L’s has the least y-intercept.
If this is true, is there any mathematical proof (especially in co-ordinate geometry)?
- pardon me for not using more specific mathematical terms.