3. Consider the following LP problem, in which slack variables have already been inserted: maximise 3x + x2 xX3 subject to 2 +x5 5 X1, X2, X3, X4, X5 0 2x1 + 2x2 -x 3x + 2x3 x3 + x4 That is, maximise cx s.t. Ax = b and x 0. = (a) For the basis x2, x3 (in that order) identify and write the basis matrix B, and verify that its inverse B-1 [32] (b) Calculate B-b and hence write the basic solution corresponding to the basis x2, X3. Is it a feasible solution? (c) Identify and write the basic cost vector c. Calculate the row vector (c3B-)A ct and hence explain why this basic solution is not optimal. (d) Explain why x is a candidate to enter the basis. Calculate the column BP where P is the column of the original matrix A. Use an appropriate ratio test to determine which basic variable would leave the basis. There is no need to execute any more calculations beyond determining which variable leaves the basis.