Question

Solve the following linear programming models graphically and explain the solution results based on the different solution types we discussed in class. a) Formulation 1 Subiect to: AX 12 X,Y 20 b) Formulation 2 Max Z = X + 4Y Subject to: 2X +3Y 3 24 Y 2 1 X,Y 2 0 c) Formulation 3 Subject to: X 2 4 6X 6Y 2 42 Y 2 2

Answer 1

a)

Graphical representation is following:

Ξ Untitled Graph Create Accountr Sign In desmos 4r 12 3ys9 12 i re 7 6 powered by desmos

In the above graph, we see that there is no feasible region, because constraint 1 and 4 are conflicting.

Therefore, this problem is infeasible.

b) Graphical representation is following:

Untitled Graph desmos 2r+3y24 x2 1 V2 1 2 powered by 四^ | desmos

Vertex points are highlighted on the graph.

Feasible region is bounded by the three vertex points.

Value of objective function is maximum at point (1,6)

Therefore, optimal solution is:

X = 1

Y = 6

Objective value Z = 1*1+4*6 = 25

Optimal solution is unique.

c)

desmos E Untitled Graph 6x + 6y2 42 У 2 4 (4, 3) (5,2) powered by 2desmos

Feasible region is unbounded.

Vertex points are highlighted on the graph.

Vale of objective function (Z) is minimum at vertex (4,3)

Therefore, optimal solution is:

X = 4

Y = 3

Objective function Z = 5*4-3*3 = 11

Solution is unique.