Problem 2: Consider the following linear program:2x1 + x2maxx1,x2 ERsubject toX1X1- 2x1X1x2+X2+ x2x21-2VI VI VI AV1остан55(4)1. Make a figure that illustrates the feasible set in R².2. Provide some integers n, m € R and matrices c E R", A € Rmxn, and b € Rm such that it is instandard form maxxER cx s.t. Ax = b and x > 0.3. On your figure, identify each vertex x € R² and its corresponding basis (possibly more than one)B of the columns of A so that N = 0 where N = {1,...,n} \ B.4. Solve the linear program using the simplex algorithm in tableau form. Report the iterations onyour figure.5. Use the dual simplex algorithm in order to find a solution if the constraint x₁ < 2 is added.

The feasible region is the shaded polygon bounded by the lines -2x1 + x2 = 1, 2x1 + x2 = 5, and x2 =…

Problem 2: Consider the following linear program: 2x1 + x2 max #1,#2 ER subject to 21 x1 -2x1 x1 + + " < 1 <5 <5 X2 X2 X2 x2 > 0 (4) 1. Make a figure that illustrates the feasible set in R². 2. Provide some integers n, m ER and matrices c ER", A € Rmxn, and be Rm such that it is in standard form maxzER cx s.t. Ax=b and x > 0.