The figure shows the graphical model or a linear program The

The figure shows the graphical model or a linear program. The large numbers on the right (1, 2, and 3) indicate the constrains. The feasible region is shaded. The variables are restricted to nonnegative values. The small numbers (0, 1, 2, and 3) indicate four feasible corner points: 0, 1, 2, 3. Three objective functions are under consideration, as indicated by the three lines labeled A, B, and C. The arrows represent the directions of increasing objective function. Objective B is parallel to constraint 3. In each case, specify the location of the optimal solution. If there is more than one optimal solution, characterize all of them. (a) Maximize A (b) Maximize B (c) Maximize C (d) Maximize A (e) Maximize B (f) Maximize C (g) Drop x_a greaterthanorequalto 0 and minimize C

Solution

(a)the point where the line A and the constraint 3 intersect is the optimal solution of the maximum A