Consider the following linear programming model with 4 regular constraints: Maximize 3X + 5Y (a) Draw your graph in the space below: subject to: 4X + 4Y 48 (constraint #1) 4X + 3Y 50 (constraint #2) 2X + 1Y 20 (constraint #3) X 2 (constraint #4) X, Y 0 (non-negativity constraints)

(a) Which of the constraints is redundant? Constraint #______. Justify by drawing a graph

(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints). Constraint #1: _______________________________________________________________ Constraint #2: _______________________________________________________________ Constraint #3: _______________________________________________________________ Constraint #4: _______________________________________________________________

(c) Which of the following points yields the best solution? Underline the best solution: (7,5), (9,2), (6,6). Justify your answer (using the data from the above LP model). (7,5): ____________________________________________________________________

(9,2): ____________________________________________________________________

(6,6): ____________________________________________________________________