Solve the linear programming problem by following the steps: (i) Graph the set of inequalities (use graph paper or a ruler to make the graph as precise as possible). (ii) Find the vertices of the feasible region. (iii) Evaluate the objective function at the vertices. (iv) State the optimal objective function value and the vertex at which the optimal value is obtained.

Maximize 7x + 5y

Subject to

2x + y < 8

x + y < 6

y > x - 1

x > 0

y > 0