Linear programming graph T/F questions

[csc2iffy]

Homework Statement

The shaded area on graph represents the feasible region of a linear programmin problem whose objective function is to be maximized.

Label each of the following statements as True or False, and then justify your answer based on the graphical method. In each case, give an example of an objective function that illustrates your answer.

(a) If (3,3) produces a larger value of the objective function than (0,2) and (6,3), then (3,3) must be an optimal solution.

(b) If (3, 3) is an optimal solution and multiple optimal solutions exist, then either (0,2) or (6,3) must also be an optimal solution.

(c) The point (0,0) cannot be an optimal solution.2. The attempt at a solution
I said...

(a) True

(b) True

(c) False

 

[Ray Vickson]

Homework Statement

The shaded area on graph represents the feasible region of a linear programmin problem whose objective function is to be maximized.

Label each of the following statements as True or False, and then justify your answer based on the graphical method. In each case, give an example of an objective function that illustrates your answer.

(a) If (3,3) produces a larger value of the objective function than (0,2) and (6,3), then (3,3) must be an optimal solution.

(b) If (3, 3) is an optimal solution and multiple optimal solutions exist, then either (0,2) or (6,3) must also be an optimal solution.

(c) The point (0,0) cannot be an optimal solution.


2. The attempt at a solution
I said...

(a) False, (3,3) cannot be an optimal solution because ? I just think it's because (6,3) would always be greater, I can't think of an example where it wouldn't be

(b) False, either (3,3) and (0,2) are optimal, or (3,3) and (6,3) are optimal.

(c) True

I need a little help justifying my answers and finding an example of an objective function illustrating my answers. Also, I'm not 100% sure they're correct to begin with... :/

(a) You are not allowed to say "I just think it's because (6,3) would always be greater..", as you were TOLD that (3,3) gave the greater value! I can think of millions of examples where (3,3) gives a larger objective value than (6,3).
(b) You are saying something is both false and true at the same time.
(c) Why?

RGV

 

[csc2iffy]

I am just learning this stuff ok! thanks for all your "help" but i figured it out