Suppose we are given a standard form LP problem: minimize f(~x) = ~cT ~x subject to: A~x = ~b ~x ~0 Consider the following vectors: ~x0 = 1 0 2 3 0 , ~r0 = 0 1 0 0 1 , ~u = 2 0 0 0 4 We are told that: ~x0 is a basic feasible solution with corresponding vector ~r0 of reduced cost coefficients, the objective function value at this basic feasible solution is f(~x0) = 6, ~u is in Nul(A). (a) Give as many values of the canonical tableau corresponding to the given basic feasible solution ~x0 as possible. Write for entries that cannot be determined from the information given. (b) Find a (not necessarily basic) feasible solution with an objective function value that is strictly less than 6.

7. Suppose we are given a standard form LP problem: minimize f@= subject to: A = 7 Consider the following vectors: 11 2 ro 0 4 We are told that: To is a basic feasible solution with corresponding vector of reduced cost coefficients, the objective function value at this basic feasible solution is f(T) = 6, is in Nul(A). (a) Give as many values of the canonical tableau corresponding to the given basic feasible solution to as possible. Write * for entries that cannot be determined from the information given. (b) Find a (not necessarily basic) feasible solution with an objective function value that is strictly less than 6. 7. Suppose we are given a standard form LP problem: minimize f@= subject to: A = 7 Consider the following vectors: 11 2 ro 0 4 We are told that: To is a basic feasible solution with corresponding vector of reduced cost coefficients, the objective function value at this basic feasible solution is f(T) = 6, is in Nul(A). (a) Give as many values of the canonical tableau corresponding to the given basic feasible solution to as possible. Write * for entries that cannot be determined from the information given. (b) Find a (not necessarily basic) feasible solution with an objective function value that is strictly less than 6