# midterm1_Qiong_prep - Problem 1: consider the following LP...

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Problem 1:consider the following LPmaxx1;x2;x3fcx1°3x2gs.t.x1°2x2±6x2°x3±1x1²0; x2²0; x3²0³can you °nd a value ofcto make the LP unbounded?³suppose that the LP has an additional constraintx3±bcan you give a value ofbto make the LP infeasible?Problem 2: Draw a feasible region of the following two-variable LPmaxx1;x2f2x1°x2gs.t.x1+x2²1x1°x2±13x1+x2±6x1²0; x2²0Determine the optimal solution to this LP, using whichever method you °nd theeasiest.Problem 3Formulate the augmented LP for the followingmaxx1;x2;x3f4x1+x2°x3gs.t.x1+ 3x2±63x1+x2°x3±9x1²0; x2²0; x3²0how many basic variables does this LP has? How many constraints (excludingnon-negativity constraints) does it dual LP has? How many basic variables doesthe dual LP has? Ifx1andx2are basic variables in the above, what is matrixB, and verify thatB°1=°°1=83=83=8°1=8±;B°1b=°21=89=8±1

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Term
Fall
Professor
Staff
Tags
LP, max fcx1, max f2x1