1. Max 2X1 + 3X2

s.t. 4X1 + 5X2 < 20 (1)

12X1 + 7X2 < 42 (2)

1X1 + 1X2 > 2 (3)

X2 > 1 (4)

X1, X2 > 0

Please 1) Draw the boundary straight line for each constraint. Must show the points used (or slope/Intercept if used).

2) Indicate what region should be selected for each of the constraints.

3) Shade the feasible region for the LP problem.

2 Max 3X1+ 4X2

s.t. 2X1 + 1.5X2 < 6 (1)

3X1 + 7X2 < 21 (2)

2X1 < 5 (3)

X1, X2>0

a. Please use the graphical method to find the FEASIBLE REGION. Please list all the points used to draw the boundary straight lines and label the 4 constraints in your graph.

b. Please draw an objective function line in the graph of a. and mark the optimal solution as a star. (must list the equation and the points used to draw the line)

c. Please get the optimal solution (Must list the system of two equations, which cross at the star): How much is X1 and X2? You need to indicate the maximized objective function output.