2. Consider the following LP: = 411 + 3.12 max subject to -2 + 2x2 > 2x1 + 3.22 C1 + 2.22 VI (A) (B) (C) (D) 10 0. S 11 22 (a) Draw and shade the feasible region in the box below. Identify each constraint line by writing the corresponding inequality (i.e. (A),...,(E) ) next to it. I 13 AN a (b) Choose a numerical value 20 for 2 so that the profit line zo = 4x1 + 3x2 can be drawn in the above box and that this line intersects the feasible region. Draw this line and label it with 2 = 20 (and thus show what the numerical value of 2 is for this line). Indicate with a small arrow the direction for this line to be shifted in order to represent a higher z-value. (c) In the box above draw and label clearly the set of all points that yield the optimal value for 2. (d) In the box below state the complete optimal solution for the LP problem defined above, i.e. identify visually the values of the decision variables and write them down together with the optimal value of the objective function. (e) Indicate which constraints from all of (A), (E), if any, are binding. I (f) If the objective function were to change to z = 211 12 would the optimal values of 11 and 22 change? Would the optimal value of 2 change? Justify your answer by drawing and labeling an extra line in the above diagram of subquestion (a) or justify otherwisee