Question

can there be more than one point in the feasible region where the maximum or minimum occurs when solving linear programming problems graphically?

Answer 1

hint:
Geometric Approach

If the slope of the objective function is negative and you take a line with that slope passing through the origin and move it to the right through the feasible region, the last corner point hit by that moving line will be the maximum value.

In the example shown, the last line with slope m=-4/3 that touches the feasible region touches at the corner point (6,3).

Since z=4(6)+3(3)=24+9=33, the maximum value is 33 when x=6 and y=3.