CHAPTER 2
LINEAR PROGRAMMING MODELS: GRAPHICAL AND
COMPUTER METHODS
SOLUTIONS TO DISCUSSION QUESTIONS
2-1. The requirements for an LP problem are listed in Section 2.2. It is also assumed that conditions of
certainty exist; that is, coefficients in the objective function and constraints are known with certainty and
do not change during the period being studied. Another basic assumption that mathematically
2-2. If we consider the feasible region of an LP problem to be continuous (i.e., we accept non-integer
2-4. A problem can be unbounded if one or more constraints are missing, such that the objective value can
be made infinitely larger or smaller without violating any constraints (refer to Section 2.6 in the chapter).
2-5. This question involves the student using a little originality to develop his or her own LP constraints
2-6. The manager’s statement indeed has merit if he/she understood the deterministic nature of LP input
data. LP assumes that data pertaining to demand, supply, materials, costs, and resources are known with
2-7. The objective function is not linear because it contains the product of X1 and X2, making it a second-
2-8. The computer is valuable in (1) solving LP problems quickly and accurately; (2) solving large
2-9. Most managers probably have Excel (or another spreadsheet software) available in their companies,
and use it regularly as part of their regular activities. As such, they are likely to be familiar with its usage.
2-11. Slack is defined as the RHS minus the LHS value for a constraint. It may be interpreted as the
2-12. An unbounded solution occurs when the objective of an LP problem can go to infinity (negative