Solving a linear program can never result in integer values for the decision variables.

Question

BlackTom AI · Accepted Answer

Question restatement: The statement says, 'Solving a linear program can never result in integer values for the decision variables.' Answer options: True or False.

Option 1: True. This claim asserts that linear programming solutions can never be integers. In fact, this is incorrect in general. Linear programs (LPs) optimize a linear objective subject to linear constraints, and their feasible region is a convex polyhedron. The optimal solution can be integer or fractional depending on the problem data. There are many LPs where the optimum occurs at an integer point, so this option misstates the reality of LP solutions.

Option 2: False. This statement denies the universal claim of impossibility and aligns with the actual behavior of LPs. While many LPs yield fractional optimal solutions, it is entirely possible for an LP to have an optimal vertex with integer values for the decision variables. For example, with integer coefficient data or in certain structured cases (like unimodular constraint matrices or when the LP relaxation of an integer program happens to be integral), the optimum can be integer. Additionally, even when non-integer optima exist, an LP can still have integer optimal solutions in some cases. The existence of integer optimal solutions demonstrates that the blanket claim 'can never' is false.

Additional nuance: The core misconception in Option 1 is treating LPs as always producing fractional outcomes or as inherently incompatible with integers. In contrast, Option 2 recognizes that integers can occur in LP solutions, even though not guaranteed for every LP, and that the possibility itself makes the statement false.

Summary of reasoning path: The claim in Option 1 overgeneralizes about LP solutions and ignores cases where the optimum is at an integer point. Option 2 accurately reflects that integers can occur in LP solutions, even if not universally true for all LPs, thereby making the statement false.

BU.520.601.T2.FA25 Final Exam

Solving a linear program can never result in integer values for the decision variables.

查看解析

登录即可查看完整答案

类似问题

Consider the following optimization problem and the constraint boundary lines given below. Maximize profit = 4X + 4Y Constraints 3X + 2Y ≤ 150 X - 2Y ≤ 10 2X + 3Y ≤150 X, Y ≥ 0 When the constraint coefficient of x in the blue constraint changes from 1 to 3, the optimal solution changes.

A constraint is binding if it left hand side of a constraint is equal to the right hand side after the optimal solution is plugged into the constraint function.

A zero in the allowable increase or decrease columns of the variable cells table in the sensitivity report indicates that

It is not possible to have more than one optimal solution to a linear programming problem.

The objective function for a LP model is 3 X 1 + 2 X 2. If X 1 = 20 and X 2 = 30, what is the value of the objective function?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单