The figure shows the graphical model of a linear program. The large numbers on t

Question

The figure shows the graphical model of a linear program. The large numbers on the right (1, 2, and 3) indicate the constraints. The feasible region is shown in white, and the infeasible region is shaded. The variables are restricted to nonnegative values. The small numbers (0, 1, 2, and 3) indicate four feasible comer 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. Maximize A Maximize B Maximize C Minimize A Minimize B Minimize C Drop x_1 greaterthanorequalto 0 and minimize C

Explanation / Answer

The three lines A , B and C represent the objective function
and all the three have arrows pointing towards the direction of increasing objective functions.

The three objective function would be either maximized or minimized at any of the 4 corner points or the
feasible points (0,1,2,3)

a> maximize A : According to the arrow direction A would be maximized at 2

b> maximize B : at point 3 B would be maximized as 3 is the only feasible point that falls in the arrow direction of line B.

c> maximize C : the direction in which C points doesn't have any feasible point and as 3 is the closest to the line C so at 3 C would be maximum.

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