Understanding Assumptions in Linear Programming Flashcards
Explore key assumptions in linear programming with engaging flashcards based on Santa's Workshop examples. (11 cards)
What is the Proportionality Assumption?
The contribution of the objective function from each decision variable is proportional to the value of the decision variable.
How does the Proportionality Assumption apply to constraints?
The contribution of each variable to the left-hand side of each constraint is proportional to the value of the variable.
Provide an example of the Proportionality Assumption from Santa’s Workshop.
The contribution to the objective function from making four soldiers (4 × 3 = R12) is exactly four times the contribution from making one soldier (R3).
What is the Additivity Assumption?
The contribution to the objective function for any variable is independent of the values of the other decision variables.
How does the Additivity Assumption apply to constraints?
The contribution of a variable to the left-hand side of each constraint is independent of the values of the other decision variables.
Provide an example of the Additivity Assumption from Santa’s Workshop.
No matter what the value of x2, the manufacture of x1 soldiers will always contribute 3x1 Rands to the objective function.
What is the Divisibility Assumption?
The Divisibility Assumption requires that each decision variable be allowed to assume fractional values.
What happens when divisibility is not present?
Rounding off each variable in the optimal LP solution to an integer may yield a reasonable solution.
Provide an example of the Divisibility Assumption from Santa’s Workshop.
The Divisibility Assumption implies that it is acceptable to produce 1.5 soldiers or 1.63 trains.
What is the Certainty Assumption?
The Certainty Assumption is that each parameter (objective function coefficient, right-hand side, and technological coefficient) is known with certainty.
Provide an example of the Certainty Assumption from Santa’s Workshop.
If we were unsure of the exact amount of carpentry and finishing hours required to build a train, the Certainty Assumption would be violated.
