3. Consider the following LP problem. max s.t. z = 2.5x1 + 6x2 1 + 2x2 0 (a) (15 points) Solve this problem using the graphical method. (b) (10 points) Consider the graph you have drawn in part (a). One of the extreme points and its corresponding basic feasible solution (BFS) is given with the list of basic and non basic variables. Fill the table with the remaining extreme points (You can draw a similar table and fill it on paper). List each of the extreme points and the corresponding BFS, the nonbasic variables and the basic variables. Extreme Point Corresponding BFS (x1,x2) (x1, x2, 91, 92) Nonbasic variables Basic variables (0,0) (0,0,30,40) 21,22 S1, S2 4. (25 points) The Whitt Window Company produces two different kinds of hand-crafted windows: a wood-framed and an aluminum-framed window. The company earns $300 profit for each wood-framed window and $400 profit for each aluminum-framed window. The resources required for producing wood-framed window and aluminum-framed window are shown below: Window Wood-framed Aluminum-framed Processing Time on Machine 1 8 hours 12 hours Processing Time on Machine 2 6 hours 7 hours Glass 2 m2 3 m2 The company owns 730 hours on machine 2. However, machine 1 should be rented from outside the company. The company can rent at most 980 hours of Machine 1 at a cost of $50/hour. There are 260 m2 of glass available for production. At least 88 wood-framed windows and at least 26 aluminum- framed windows should be produced. Let