Question: LP Graphical Method: Consider the two-variable Linear Program below: min 15x1 + 20x2 s.t. x1 + 2x2 10 2x1 3x2 6 x1 + x2 6

LP Graphical Method: Consider the two-variable Linear Program below:

min 15x1 + 20x2

s.t. x1 + 2x2 10

2x1 3x2 6

x1 + x2 6

x1 0, x2 0

(a) Use the graphical method to solve the Linear Program (provide optimal solution and optimal value of the problem)

(b) To what class does this Linear Program belongs (feasible or infeasible?, bounded or unbounded?, unique or multiple optimal solutions?)

(c) Suppose that you are allowed to change (only) the objective coefficient of x1 (15 in the original problem) in the Linear Program. What value of the objective coefficient of x1 would lead to a problem that is unbounded (unbounded objective)?

(d) What would be the optimal solution of the Linear Program if suddenly we are told that the second constraint of the Linear Program must be satisfied with equality, instead of inequality; namely, instead of 2x1 3x2 6 we have 2x1 3x2 = 6.

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