The following tableau represents a specific simplex iteration. All variables are nonnegative. The tableau is not optimal for either a maximization or a minimization problem. Basic Variable Row No. Coefficient of Right z ! ! ! ! ! ! ! ! Side z 0 1 0 5 0 4 1 10 0 0 620 ! ! ! 1 2 3 0 0 0 0 3 0 2 3 0 1 1 3 1 1 1 0 0 6 1 0 4 5 1 3 0 0 0 12 6 0 (i) Categorize the variables as basic and non basic and provide the current values of all the variables. [4] (ii) Assuming that the problem is of the maximization type, identify the non basic variables that have the potential to improve the value of . If each such variable enters the basic solution, determine the associated leaving variable, if any, and the associated change in . Do not use Gauss Jordan row operations. [7] (iii) Repeat part (ii) assuming that the problem is of the minimization type. [3]