1. Max 2X1 + 3X2 s.t. 6X1 + 3X2 < 18 (1) 4X1 + 8X2 < 32 (2) 1X1 + 2X2 > 2 (3) X1 > 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 3 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.