Question: Problem 1. Consider the following LP: maximize 2x1 X2 subject to X1 + x2 > 1 21 22 = 1 3x1 + x2 0 (constraint

Problem 1. Consider the following LP: maximize

Problem 1. Consider the following LP: maximize 2x1 X2 subject to X1 + x2 > 1 21 22 = 1 3x1 + x2 0 (constraint 1) (constraint 2) (constraint 3) (a) [2pt] Is the LP in standard form? If not, write the standard form of the LP. (b) [4pt] Draw the feasible region. (c) [2pt] Determine the optimal solution and the optimal objective value to this LP, using whichever method you find the easiest. (d) [2pt] Suppose we change the objective function to: maximize cx1 X2 Can you find a value of c to make the LP have infinitely many optimal solutions? (e) [2pt] Suppose that the LP has an additional constraint: x2 > b. Can you give a value of b to make the LP infeasible

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