# LP graphical method true/false Q

1. Jan 29, 2012

### csc2iffy

1. The problem statement, all variables and given/known data
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. Relevant equations
I posted the attachment of the picture

3. 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.

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