Question

Problem 1: Consider the following linear optimization problem: max +22 +rs subject to X1 + X2 + X3 = 10 2x1 - 22 24 i 20, 1,2,3. (a) Bring the problem to a standard form. (b) Show that the point (2,8,0)Ts optimal by the optimality condition of the linear program- ming. Is it an extreme point? Provide arguments for your answers. (c) Determine at least one other point different than (2,8,0)T, which is an extreme point of the constraint set (1). (d) Find all solutions (Hint: solve the problem geometrically.)

Answer 1

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