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FE · 9% of the exam

Modeling and Quantitative Analysis practice questions

10 free Modeling and Quantitative Analysis questions for the FE Industrial and Systems Exam (FE) exam, each with the correct answer and an explanation for every option.

Start the questionsFree 10-question FE quiz

What this domain covers

Building and solving models for decisions: optimisation, decision analysis, risk, queuing, Markov chains and simulation.

Exam weight
9%
On a real exam
≈ 10 questions
In our bank
54 questions

Topics that come up most

  • Linear and integer programming formulation
  • Decision trees and expected value
  • Queuing models and performance measures
  • Markov chains and steady-state probabilities
  • Simulation and data modelling

How to study it

Practise writing the objective function and constraints from a short word problem; formulation is tested more often than solving by hand.

Sample Modeling and Quantitative Analysis questions

Try each one before opening the answer. Original questions written to the official exam objectives.

  1. Question 1

    In a newsvendor problem, underage cost is $6 per unit and overage cost is $2 per unit. The critical ratio is:

    • A0.33
    • B0.25
    • C3
    • D0.75
    Show answer and explanation

    Answer: D) 0.75

    • AIncorrect. That's C_o ÷ C_u.
    • BIncorrect. That's C_o ÷ (C_u + C_o).
    • CIncorrect. That's C_u ÷ C_o.
    • DCorrect. C_u ÷ (C_u + C_o).

  2. Question 2

    In a decision tree analysis for a risk-neutral decision maker, at each decision node you choose the branch with the:

    • AHighest expected monetary value
    • BHighest single possible payoff
    • CLowest cost regardless of outcome
    • DMost branches
    Show answer and explanation

    Answer: A) Highest expected monetary value

    • ACorrect. Chance nodes are averaged; decision nodes take the best.
    • BIncorrect. That's an optimistic rule.
    • CIncorrect. Use expected value.
    • DIncorrect. Use expected value.

  3. Question 3

    A two-variable LP has corner points (0, 0), (4, 0), (2, 2) and (0, 3). The maximum of 3x + 2y is:

    • A10 at (2, 2)
    • B12 at (4, 0)
    • C6 at (0, 3)
    • D0 at (0, 0)
    Show answer and explanation

    Answer: B) 12 at (4, 0)

    • AIncorrect. 12 is larger.
    • BCorrect. Evaluate each corner: 3(4) + 2(0) = 12 is the largest.
    • CIncorrect. 12 is larger.
    • DIncorrect. That's the minimum.

  4. Question 4

    A minimal spanning tree of a network:

    • AIncludes every arc
    • BFinds the shortest path between two nodes
    • CMaximizes flow
    • DConnects all nodes with the minimum total arc length
    Show answer and explanation

    Answer: D) Connects all nodes with the minimum total arc length

    • AIncorrect. It uses n − 1 arcs.
    • BIncorrect. That's shortest path.
    • CIncorrect. That's max flow.
    • DCorrect. Used for cable or pipeline layouts.

  5. Question 5

    A labor constraint has a shadow price of $5 per hour. Adding 10 hours (within the valid range) changes the optimal profit by:

    • ANo change
    • BA $5 increase
    • CA $50 decrease
    • DA $50 increase
    Show answer and explanation

    Answer: D) A $50 increase

    • AIncorrect. A binding constraint has value.
    • BIncorrect. That's per hour.
    • CIncorrect. More of a binding resource helps.
    • DCorrect. Shadow price × change.

  6. Question 6

    A balanced transportation problem is one in which:

    • AThere's only one source
    • BAll costs are equal
    • CEvery route is used
    • DTotal supply equals total demand
    Show answer and explanation

    Answer: D) Total supply equals total demand

    • AIncorrect. It's about supply and demand.
    • BIncorrect. It's about supply and demand.
    • CIncorrect. It's about supply and demand.
    • DCorrect. A dummy node balances an unbalanced problem.

  7. Question 7

    A balanced transportation problem has 3 sources and 4 destinations. How many basic variables does a nondegenerate basic feasible solution contain?

    • A5
    • B7
    • C12
    • D6
    Show answer and explanation

    Answer: D) 6

    For an m × n balanced transportation problem, one supply/demand constraint is redundant, so a basic solution has m + n − 1 basic variables: 3 + 4 − 1 = 6.

    • AIncorrect. This subtracts 2 from m + n. A transportation basis has exactly one redundant constraint, so the count is m + n − 1 = 6.
    • BIncorrect. 7 is m + n, the number of supply and demand constraints. One of those constraints is redundant because total supply equals total demand, so there are m + n − 1 = 6 basic variables.
    • CIncorrect. 12 is m × n, the total number of cells (decision variables). Only a subset of them are basic.
    • DCorrect. A basic feasible solution has m + n − 1 = 3 + 4 − 1 = 6 basic variables. Nondegenerate means all 6 are strictly positive.

  8. Question 8

    In a simulation, demand is 0 for random numbers 0.00–0.19, 1 for 0.20–0.69 and 2 for 0.70–0.99. A random number of 0.73 gives a demand of:

    • A0
    • B1
    • C2
    • D0.73
    Show answer and explanation

    Answer: C) 2

    • AIncorrect. That range ends at 0.19.
    • BIncorrect. That range ends at 0.69.
    • CCorrect. 0.73 falls in 0.70–0.99.
    • DIncorrect. Map the random number to a demand.

  9. Question 9

    The max-flow min-cut theorem states that the maximum flow through a network equals:

    • AThe shortest path length
    • BThe sum of all arc capacities
    • CThe capacity of the minimum cut
    • DThe number of nodes
    Show answer and explanation

    Answer: C) The capacity of the minimum cut

    • AIncorrect. It's the minimum cut capacity.
    • BIncorrect. It's the minimum cut capacity.
    • CCorrect. A cut separates source from sink.
    • DIncorrect. It's the minimum cut capacity.

  10. Question 10

    An M/M/1 queue has λ = 6 per hour and μ = 8 per hour. The average number waiting in the queue is:

    • A2.25
    • B3, the number in system
    • C0.75, the utilization
    • D0.375
    Show answer and explanation

    Answer: A) 2.25

    • ACorrect. \(L_q = \rho^2/(1 - \rho)\) with ρ = 0.75.
    • BIncorrect. L = ρ/(1 − ρ) = 3 includes the one in service.
    • CIncorrect. That's ρ.
    • DIncorrect. That isn't the calculation.

Modeling and Quantitative Analysis: FAQs

How much of the FE exam is Modeling and Quantitative Analysis?

Modeling and Quantitative Analysis is 9% of the FE exam by the official exam guide's weighting, which on a 110-question form works out to roughly 10 questions. The real exam's exact split varies by form.

What does the Modeling and Quantitative Analysis domain cover?

Building and solving models for decisions: optimisation, decision analysis, risk, queuing, Markov chains and simulation.

How should I study Modeling and Quantitative Analysis for FE?

Practise writing the objective function and constraints from a short word problem; formulation is tested more often than solving by hand.

Where can I practise more Modeling and Quantitative Analysis questions?

This page has 10 free Modeling and Quantitative Analysis questions with answers. The ExamWize FE question bank has 54 questions in this domain. Every practice exam result breaks your score down by domain, and Review Mode re-drills the questions you missed.

Other FE topics

Also: 15 free questions across all topics, the FE cheat sheet and the study guide.

Get Modeling and Quantitative Analysis exam-ready

The full FE bank has 54 Modeling and Quantitative Analysis questions. Timed practice exams match the real exam's length and domain weights, every result shows your score per domain, and Review Mode re-drills the questions you missed.

See the full FE practice examsTake the free diagnostic

Not affiliated with NCEES; questions are original, written from the official exam outline, and never copied from the real exam.