Consider the following Linear Programming model: Maximize x+0.5y
Subject to
2y-x<=4
2x+5y<=20
x+2y>=2
2x-y<=8
x>=1
y<=3
x>=0,
y>=0
(a) Draw the feasible region and objective function for the model. Show the optimal solution and optimal value. Justify why the solution is optimal.
(b) What other method can you use to find the optimal solution without drawing the objective function? Considering the structure of the feasible region, which method is better? Justify your answer.