(4 pts) 5. Find a solution to the following linear program using the graphical technique: min z= 4x1 + X2 s.t 2x1 + 3x2 6x2 X1 12 6 0 0 (1) (2) (3) X1 X2 a) Graph the problem and shade in the feasible region. Label the axes and all constraints. b) What is the optimal solution and what is the value of the objective? c) Label all the basic solutions. How many are there? For each basic solution indicate 1) Which variables are basic and which are nonbasic. 2) The value of each variable. 3) Is the solution feasible or not. d) What are the x1 and x2 coordinates of the optimal solution(s)? e) What is the z-value of the optimal solution(s)? Consider parts e, f, and g separately. f) How would the feasible region and/or optimal solution change if we deleted the second constraint? How would the feasible region and/or optimal solution change if we let x2 be unrestricted in sign (can take on negative values)? h) How would the feasible region and/or optimal solution change if the second constraint was > instead of