How Things Can Go Wrong In
The Linear Programming Formulation and Solution:
Problem 2.7 Case
A. Formulation of the problem is wrong.
1.1. The objective function was missing. Every LP problem has an objective function. The objective function (Maximize or minimize), can be constructed by using the information the word problem description (for this problem, the last the last paragraph?)
1.2. Combining constraints in the formulation stage:
X1 £ 500 and X2 £ 500 IS NOT same as
X1 + X2 £ 1000
1.3. The inequality constraints are misrepresented: For example, instead of X1 £ 500, the constraint X1 < 500 is used. Notice that in LP formulation the constraints are always in the form of ³, or, =, or £ . Never >, or <.
1.4. Missing constrains in the formulation stage; for example X1 £ 500 and X2 £ 500 were missing.
1.5 Directions of some inequality constraints were wrong: For example, instead of
X1 £ 500, the constraint X1 ³ 500 is used.
1.6. Non-negativity conditions were missing. In many LP problems, the non-negativity conditions are called the implied conditions or constraints. We will see in our next week solution to this problem, how this condition make the feasible region much smaller when searching for the best production strategy. Clearly, this condition enforce the computer implementation not to select negative numbers, therefore, improves efficiency too.
B. Graphical Solution Went Wrong:
2. The boundary lines of the feasible region should be the constraints at their binding (=) position NOT ³, or £.
3. Ignored or missed some constraints in the solution algorithms: Graphical and Algebraic Method.
4. The computer output report was handed in without any managerial explanations. I do not need any printout without explanation. You as a Management Scientist should never submit a print out to the Manager (i.e., decision maker) without enough explanation of what those numbers mean in simple the language (no keywords or phrases) understandable the manager. That is, the same language and style the problem was described in words.
5. Got the solution from the computer package and then found the optimal point by solving one system of equations. The correct graphical approach as outlined in your lecture note, is as follow: since the feasible region is bounded, then solution is one of the vertices. Which vertex is the optimal? You need to find the coordinate of all feasible corner point, then evaluate the objective function, then to see which one provides the maximum value. This way we determine the optimal strategy and then the optimal value.
6. To have a unified standard for presenting graphical solution, it is customary (as in your textbook, and your lecture notes) to have X1, and X2 as the horizontal and vertical axis, respectively (not the other way round). Unfortunately, some ignored this practice.