A Short Course in Linear Programming

 

Lesson 4. What do the solutions mean?

Use the Mathematical Programming Glossary to look up terms you do not understand, such as those in italics. 
 
  1. Review all of the introductions cited in previous lessons.
  2. Experiment with Anima-LP (java needed).
  3. Answer the questions about the diet problem raised in lesson 1.

    4. Solution.
  4. Continue to browse the glossary and look particularly at the following entries.
Exercise: Formulate the following (sparse capacitated transportation problem) as an LP. Then, describe the model in MODLER (or in AMPL, GAMS, XPRESS-LP, ...).
 
Given: a set of sources, I;  a set of destinations, J; 
  a set of arcs, A={(i, j): i in I and j in J}; 
supplies, S(i): i in I;  demands, D(j): j in J; 
costs, c(i, j) and capacities, U(i, j): (i, j) in A.

Find flows, x(i, j) for (i, j) in A, that minimize total cost, subject to satisfying the demand requirements within the supply and capacity limits.
Solution.

Prove each of the following:

  1. Two suppliers that ship to the same consumer have supply prices that differ by the transporation costs.

    2. Solution.
  2. Two consumers that receive from the same supplier have prices that differ by the transporation costs.

    3. Solution.
Explain how these inferences differ for an interior solution versus a basic solution.
Solution.
 

Last updated: March 6, 1997