1
ISYE 6501 Midterm 2 Practice Exam (100 Questions)
Section 1: Optimization & Mathematical Programming (Questions 1–25)
1. What are the three main components of an optimization model?
A. Variables, constraints, objective function
B. Data, model, prediction
C. Input, process, output
D. States, decisions, probabilities
Answer: A
2. In an optimization model, what is a "feasible solution"?
A. Any solution that satisfies all constraints
B. The best possible solution
C. A solution that maximizes the objective
D. A solution that minimizes the objective
Answer: A
3. What is the order of optimization problems from fastest to slowest to solve?
A. Linear programs, convex quadratic programs, convex programs, integer programs, general
non-convex programs
B. Integer programs, linear programs, convex programs, non-convex programs
C. Non-convex programs, integer programs, convex programs, linear programs
D. Convex programs, linear programs, integer programs, non-convex programs
Answer: A
4. What is a linear program?
A. f(x) is a linear function; constraint set X is defined by linear equations and inequalities
B. f(x) is a quadratic function; constraints are non-linear
C. f(x) is a convex function; constraints are integer
D. f(x) is a non-convex function; constraints are linear
Answer: A
5. What is a convex quadratic program?
A. f(x) is a convex quadratic function; constraint set X is defined by linear equations and
inequalities
B. f(x) is a linear function; constraints are non-linear
C. f(x) is a non-convex function; constraints are integer
D. f(x) is a concave function; constraints are linear
Answer: A
6. Are convex optimization problems guaranteed to find the optimal solution?
A. Yes
B. No; they might converge to a local optimum
, 2
C. Only if the objective is linear
D. Only if all variables are binary
Answer: A
7. Are non-convex optimization problems guaranteed to find an optimal solution?
A. Yes, always
B. No; they might converge to a local optimum or an infeasible solution
C. Only if the problem is small
D. Only if integer variables are used
Answer: B
8. What is an integer program?
A. A linear program plus some (or all) variables restricted to take only integer values
B. A non-linear program with continuous variables
C. A convex program with no constraints
D. A simulation model
Answer: A
9. True or False: Requiring some variables in a linear program to take integer values can
make it take a lot longer to solve.
A. True
B. False
Answer: A
10. What is a heuristic?
A. An algorithm that is not guaranteed to find the absolute best (optimal) solution
B. An algorithm guaranteed to find the optimal solution
C. A type of linear program
D. A simulation method
Answer: A
11. What is a greedy algorithm?
A. Algorithm that makes the immediately-best choice at each step
B. Algorithm that considers all future options before deciding
C. Algorithm that randomly selects variables
D. Algorithm guaranteed to find the global optimum
Answer: A
12. In a diet problem, let xi be the amount of food i eaten, and yi be binary variables
indicating if food i is eaten. Which constraint corresponds to "Unless peanut butter is
eaten, no amount of broccoli can be eaten"?
A. Xbroccoli ≤ M × Ypeanut_butter
B. Xbroccoli ≥ M × Ypeanut_butter
C. Ybroccoli ≤ Ypeanut_butter
, 3
D. Xbroccoli + Ypeanut_butter ≤ M
Answer: A
13. Which constraint corresponds to "No more than two of broccoli, cheese sauce, and
peanut butter may be eaten"?
A. Ybroccoli + Ycheese_sauce + Ypeanut_butter ≤ 2
B. Ybroccoli + Ycheese_sauce + Ypeanut_butter ≥ 2
C. Ybroccoli = Ycheese_sauce = Ypeanut_butter
D. Ybroccoli × Ycheese_sauce × Ypeanut_butter ≤ 2
Answer: A
14. Which constraint corresponds to "Either cheese sauce or peanut butter (or both) must
be eaten with broccoli"?
A. Ybroccoli ≤ Ycheese_sauce + Ypeanut_butter
B. Ybroccoli ≥ Ycheese_sauce + Ypeanut_butter
C. Ybroccoli = Ycheese_sauce = Ypeanut_butter
D. Ybroccoli + Ycheese_sauce + Ypeanut_butter ≤ 1
Answer: A
15. What are common network models?
A. Shortest path, assignment, maximum flow
B. Linear, quadratic, integer
C. Descriptive, predictive, prescriptive
D. States, decisions, probabilities
Answer: A
16. What are the constraints in network models?
A. Flow into node = flow out of node; flow on arc between min and max allowable
B. Flow into node ≠ flow out of node
C. No constraints exist
D. Only maximum flow constraints
Answer: A
17. What do we get without constraints in a network model if data is all integers?
A. An optimal solution where all variables have integer values
B. A fractional solution
C. No solution
D. An infeasible solution
Answer: A
18. Why are statistical models like linear regression more widely used than optimization
models?
A. Statistical models just need data; optimization models are hard to build and not easily
automated
ISYE 6501 Midterm 2 Practice Exam (100 Questions)
Section 1: Optimization & Mathematical Programming (Questions 1–25)
1. What are the three main components of an optimization model?
A. Variables, constraints, objective function
B. Data, model, prediction
C. Input, process, output
D. States, decisions, probabilities
Answer: A
2. In an optimization model, what is a "feasible solution"?
A. Any solution that satisfies all constraints
B. The best possible solution
C. A solution that maximizes the objective
D. A solution that minimizes the objective
Answer: A
3. What is the order of optimization problems from fastest to slowest to solve?
A. Linear programs, convex quadratic programs, convex programs, integer programs, general
non-convex programs
B. Integer programs, linear programs, convex programs, non-convex programs
C. Non-convex programs, integer programs, convex programs, linear programs
D. Convex programs, linear programs, integer programs, non-convex programs
Answer: A
4. What is a linear program?
A. f(x) is a linear function; constraint set X is defined by linear equations and inequalities
B. f(x) is a quadratic function; constraints are non-linear
C. f(x) is a convex function; constraints are integer
D. f(x) is a non-convex function; constraints are linear
Answer: A
5. What is a convex quadratic program?
A. f(x) is a convex quadratic function; constraint set X is defined by linear equations and
inequalities
B. f(x) is a linear function; constraints are non-linear
C. f(x) is a non-convex function; constraints are integer
D. f(x) is a concave function; constraints are linear
Answer: A
6. Are convex optimization problems guaranteed to find the optimal solution?
A. Yes
B. No; they might converge to a local optimum
, 2
C. Only if the objective is linear
D. Only if all variables are binary
Answer: A
7. Are non-convex optimization problems guaranteed to find an optimal solution?
A. Yes, always
B. No; they might converge to a local optimum or an infeasible solution
C. Only if the problem is small
D. Only if integer variables are used
Answer: B
8. What is an integer program?
A. A linear program plus some (or all) variables restricted to take only integer values
B. A non-linear program with continuous variables
C. A convex program with no constraints
D. A simulation model
Answer: A
9. True or False: Requiring some variables in a linear program to take integer values can
make it take a lot longer to solve.
A. True
B. False
Answer: A
10. What is a heuristic?
A. An algorithm that is not guaranteed to find the absolute best (optimal) solution
B. An algorithm guaranteed to find the optimal solution
C. A type of linear program
D. A simulation method
Answer: A
11. What is a greedy algorithm?
A. Algorithm that makes the immediately-best choice at each step
B. Algorithm that considers all future options before deciding
C. Algorithm that randomly selects variables
D. Algorithm guaranteed to find the global optimum
Answer: A
12. In a diet problem, let xi be the amount of food i eaten, and yi be binary variables
indicating if food i is eaten. Which constraint corresponds to "Unless peanut butter is
eaten, no amount of broccoli can be eaten"?
A. Xbroccoli ≤ M × Ypeanut_butter
B. Xbroccoli ≥ M × Ypeanut_butter
C. Ybroccoli ≤ Ypeanut_butter
, 3
D. Xbroccoli + Ypeanut_butter ≤ M
Answer: A
13. Which constraint corresponds to "No more than two of broccoli, cheese sauce, and
peanut butter may be eaten"?
A. Ybroccoli + Ycheese_sauce + Ypeanut_butter ≤ 2
B. Ybroccoli + Ycheese_sauce + Ypeanut_butter ≥ 2
C. Ybroccoli = Ycheese_sauce = Ypeanut_butter
D. Ybroccoli × Ycheese_sauce × Ypeanut_butter ≤ 2
Answer: A
14. Which constraint corresponds to "Either cheese sauce or peanut butter (or both) must
be eaten with broccoli"?
A. Ybroccoli ≤ Ycheese_sauce + Ypeanut_butter
B. Ybroccoli ≥ Ycheese_sauce + Ypeanut_butter
C. Ybroccoli = Ycheese_sauce = Ypeanut_butter
D. Ybroccoli + Ycheese_sauce + Ypeanut_butter ≤ 1
Answer: A
15. What are common network models?
A. Shortest path, assignment, maximum flow
B. Linear, quadratic, integer
C. Descriptive, predictive, prescriptive
D. States, decisions, probabilities
Answer: A
16. What are the constraints in network models?
A. Flow into node = flow out of node; flow on arc between min and max allowable
B. Flow into node ≠ flow out of node
C. No constraints exist
D. Only maximum flow constraints
Answer: A
17. What do we get without constraints in a network model if data is all integers?
A. An optimal solution where all variables have integer values
B. A fractional solution
C. No solution
D. An infeasible solution
Answer: A
18. Why are statistical models like linear regression more widely used than optimization
models?
A. Statistical models just need data; optimization models are hard to build and not easily
automated
