Problem C1 Consider the following linear program: Min a+b+c+d+e+f St 3b +c-d +2f=1 -b + 2d +e-f=2 a + 3d + 2f=4 a, b, c, d, e, f > 0 a) What is the A matrix? b vector? x vector? b) Consider the set of basic variables B = {a, c, d}. What is the AB matrix? What is its inverse? c) What is the corresponding set N of non-basic variables? d) For each potential pivot variable p in N, what is Ap? e) For each p in N, compute dpP = -A8-Ap, the elements of the direction vector d associated with the basic variables. f) For each p in N, what is the whole direction vector d'associated with both the basic variables and the non-basic variables? Problem C1 Consider the following linear program: Min a+b+c+d+e+f St 3b +c-d +2f=1 -b + 2d +e-f=2 a + 3d + 2f=4 a, b, c, d, e, f > 0 a) What is the A matrix? b vector? x vector? b) Consider the set of basic variables B = {a, c, d}. What is the AB matrix? What is its inverse? c) What is the corresponding set N of non-basic variables? d) For each potential pivot variable p in N, what is Ap? e) For each p in N, compute dpP = -A8-Ap, the elements of the direction vector d associated with the basic variables. f) For each p in N, what is the whole direction vector d'associated with both the basic variables and the non-basic variables