Question

2- The Lofton Company has developed the following linear programming problem with the following functional constraints.

Max x1 + x2
s.t. 2x1 + x2 ≤ 10
  2x1 + 3x2 ≤ 24
  3x1 + 4x2 ≥ 36

After running the solver, they found it infeasible so in revision, Lofton drops the original objective and establishes the three goals:

Goal 1: Don't exceed 10 in constraint 1.
Goal 2: Don't fall short of 36 in constraint 3.
Goal 3: Don't exceed 24 in constraint 2.

Please rewrite the functional constraints as the goals. Please draw the graph for the problem and show the feasible region in the graph.

Answer 1

Functional constraints are rewritten as goals as follows:

Goal 1: 2x1+x2-e1+s1 = 10

Goal 2: 3x1+4x2-e2+s2 = 36

Goal 3: 2x1+3x2-e3+s3 = 24

x1, x2, e1, e2, e3, s1, s2, s3 >= 0, where ei, si are excess and shortage for respective constraint.

Graph is following:

Create Account or Sign In desmOS E Untitled Graph 12 2x+ys 10 3x 4y2 36 0 2x+3y 24 10 12 14 16 18 2 powered by desmos

The feasible region for each constraint are highlighted in respective color.

A possible feasible is following (bounded by highlighted points) depending on priority of the goals.

E Untitled Graph desmos Create Ac 2x +ys10 3x 4y 236 2r 3y 24 (0,9) (0.8, 8.4) (0, 8) owered by desmos 6 8 10 14