Please answer all the part. it is liner and nonlinear optimization

4. Answer the following questions along with a concise explanation with respect to the linear program to maximize cx subject to x EX={x: Ax = b, x>0}, where A is mxn of rank m 0 for an associated basis? c. If there exists a d such that Ad = 0, d > 0, and cd > 0, then is the optimal objective value unbounded? d. Let be a feasible solution with exactly m positive components. Is i necessarily an extreme point of X? e. If a nonbasic variable xk has zk Ck = 0 at optimality, then can one claim that alternative optimal solutions exist? f. If xi and x2 are adjacent points and if Bi and B2 are respective associated bases, then these bases are also adjacent. True or false? Explain. g. Is it possible for an optimal solution to have more than m positive variables? h. Suppose that n=m+1. What is the least upper bound on the number of extreme points and feasible bases? i. Ap-dimensional polyhedron can have at most p extreme directions. True or false? Explain. j. Let be an extreme point having (m 1) positive components. Then there are (p+1) bases associated with this extreme point, where p=n-m. True or false? (Assume that Ax = b does not imply any variable to be a constant.) Explain<.>