B1 Consider the following linear programming problem: (5) Maximise z = x1 + 4x2 subject to X1 + 2x2 0. (8) (a) Draw the feasible region. Label all the basic solutions, and indicate, for each one, which are the basic variables. (Use our standard notation for slack variables. You do not have to find the values of the basic variables.) [4] (c) Using your solutions to the previous parts, answer the following questions about the simplex algorithm: (i) When entering a variable, why do we choose the column with the most negative z-row entry? In terms of your diagram of the feasible region, what is the meaning of the z-row entries? (ii) When exiting a variable, why do we choose the row with the smallest non- negative 0-ratio? In terms of your diagram of the feasible region, what is the geometric meaning of the 6-ratio (when this is non-negative)? [4]