Consider the following linear programming problem:

minimize 3×1 + 4.22
subject to
x1 +x2 > 120
3.×1 +2×2 > 360
x1 +2×2 > 190
x1,x2 > 0
(a) (119) Draw the feasible region. On your graph, clearly show which line corresponds to which constraint, and highlight the feasible region. (b) (396) Draw the line 3.11 + 4.12 = 12 * D on the feasible region you found in part (a), where D is the last two digits of your student ID number. For example, if your student ID is 12345, then you should draw the line 3×1 +412 = 540. Please do not forget to write down the value D. (You DO NOT need to draw again the feasible region). () (69) Find an optimal solution to the mathematical model given above using the graphical solution method. Report the optimal solution (optimal values of the decision variables) and its objective function value. Clearly show how you obtained the optimal solution.

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