# BIT 3434 Virginia Tech | Test 1 2 3 | Advanced Modeling

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**Advanced Modeling for Business Analytics**

**BIT 3434 Virginia Tech Quiz All Test 1 to 3 Solutions**

**Test 1 Questions**

Question 1

In a decisionmaking problem, anchoring effects occur when

Question 2

In the following expression, which is (are) the dependent variable(s)? PROFIT = REVENUE – EXPENSES

Question 3

In a decisionmaking framework presented in Chapter One, the term “poetic justice” refers to a situation when the following occur:

Question 4

Framing effect refers to:

Question 5

The constraint for resource 1 is

5 X1 + 4 X2 ≤ 200

If X1 = 20, what it the maximum value for X2?

Question 6

The constraints of an LP model define the

Question 7

Level curves are used when solving LP models using the graphical method. To what part of the model do level curves correspond?

Question 8

When do alternate optimal solutions occur in LP models?

Question 9

A redundant constraint is one which

Question 10

If there is no way to simultaneously satisfy all the constraints in an LP model the problem is said to be

Question 11

A facility produces two products. The labor constraint (in hours) is formulated as: 350×1+300×2 ≤ 10,000. The number 10,000 represents

Question 12 of 33 3.0 Points

Suppose that a constraint 4×1+6×2 ≥ 1,800 is binding. Then, a constraint 2×1+3×2 ≥ 600 is

Question 13

The following linear programming problem has been written to plan the production of two products. The company wants to maximize its profits.

X1 = number of product 1 produced in each batch

X2 = number of product 2 produced in each batch

MAX: 150 X1 + 250 X2

Subject to: 4/17

2 X1 + 5 X2 ≤ 200

3 X1 + 7 X2 ≤ 175

X1, X2 ≥ 0

How many units of resource one (the first constraint) are used if the company produces 10 units of product 1 and 5 units of product 2?

Question 14

Solve the following LP problem graphically using level curves.

MAX: 5 X1 + 6 X2

Subject to:

3 X1 + 8 X2 ≤ 48

12 X1 + 11 X2 ≤ 132

2 X1 + 3 X2 ≤ 24

X1, X2 ≥ 0

Question 15

Consider the following LP model:

Max Z = 30X1 + 70X2

4X1 + 10X2 ≤ 80

14X1 + 8X2 ≤ 112

X1 + X2 ≤ 10

4X1 16X2 ≤ 16

X1, X2 ≥ 0

What is the slope of the fourth constraint?

Question 16

For the model in problem 15, the optimal solution is at the intersection of constraints:

Question 17

For the model in problem 15, the optimal solution values are

Question 18

Using the refinery problem described below, which of the following is the best (most logical) objective function?

Question 19

Using the refinery problem described below, for the blending recipe for regular gas, which of the following constraints is correct?

Question 20

Using the refinery problem described below, for the maximum component availability, which of the following constraints is correct?

Question 21

Using the refinery problem described below, for the desired production level, which constraint is correct?

Question 22

A major electronics producer produces three primary products. Their planning problem, solution, and sensitivity report are shown below. Which constraints are binding?

Question 23

A major electronics producer produces three primary products. Their planning problem, solution, and sensitivity report are shown below. Suppose you have been paying your “testers” $12 per hour. What is the most you would be willing to pay them to work overtime?

Question 24

A major electronics producer produces three primary products. Their planning problem, solution, and sensitivity report are shown below. Suppose we schedule 10 fewer hours of packing? Which of the following is the new profit?

Question 25

A major electronics producer produces three primary products. Their planning problem, solution, and sensitivity report are shown below. What unit profit would have to be made from PDAs before you should consider producing them?

Question 26

A major electronics producer produces three primary products. Their planning problem, solution, and sensitivity report are shown below. If the company changed the selling price of PCs such that the profit margin changed to $39, what would happen to the optimal values of the decision variables?

Question 27

A major electronics producer produces three primary products. Their planning problem, solution, and sensitivity report are shown below. If the company changed the selling price of PCs such that the profit margin changed to $39, what would happen to the overall profit?

Question 28

A major electronics producer produces three primary products. Their planning problem, solution, and sensitivity report are shown below. How much would we be willing to pay for another assembly hour?

Question 29

A major electronics producer produces three primary products. Their planning problem, solution, and sensitivity report are shown below. If the square feet of storage changed to 43, would this affect the solution?

Question 30

A binding greater than or equal to (≥) constraint in a minimization problem means that

Question 31

If the allowable increase for a constraint is 100 and we add 110 units of the resource what happens to the objective function value?

Question 32

A change in the right hand side of a constraint changes

Question 33

The solution to an LP problem is degenerate if zero.

**BIT 3434 Virginia Tech Quiz**

**Test 2 Questions**

Question 1

A node which can both send to and receive from other nodes is a

A. demand node.

B. supply node.

C. random node.

D. transshipment node.

Question 2

Supply quantities for supply nodes in a transshipment problem are customarily indicated by

A. positive numbers.

B. negative numbers.

C. imaginary numbers.

D. either positive or negative numbers.

Question 3

What is the correct constraint for node 2 in the following diagram?

A. X12 + X23 = 100

B. X12 − X23 ≤ 100

C. −X12 + X23 ≥ 100

D. X12 − X23 ≥ 100

Question 4

The constraint X13 + X23 − X34 ≥ 50 indicates that

A. 50 units are required at node 3.

B. 50 units will be shipped from node 3.

C. 50 units will be shipped in from node 1.

D. 50 units must pass through node 3.

Question 5

Which balance of flow rule should be applied at each node in a network flow problem when Total Supply > Total Demand?

A. Inflow − Outflow ≤ Supply or Demand

B. Inflow − Outflow ≥ Supply or Demand

C. Inflow − Outflow = Supply or Demand

D. Inflow − Supply ≥ Outflow or Demand

Question 6

What formula would be entered in cell G18 in this Excel model?

Question 7

How could a network be modified if demand exceeds supply?

A. add extra supply arcs

B. remove the extra demand arcs

C. add a dummy supply

D. add a dummy demand

Question 8

What is the interpretation of units “shipped” along arcs from dummy supply nodes to demand nodes?

A. Indicates unmet demand at demand nodes

B. Indicates unmet supply at demand nodes

C. Indicates unmet demand at supply nodes

D. Indicates unmet supply at supply nodes

Question 9

The right hand side value for the ending node in a shortest path problem has a value of

A. −1

B. 0

C. 1

D. 2

Question 10

What is the constraint for node 2 in the following shortest path problem?

A. −X12 − X13 = 0

B. X12 − X24 = 1

C. X12 + X13 = 0

D. X12 − X24 = 0

Question 11

An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 24. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network representation depicts this problem. What is the balance of flow constraint for node 3 (Refinery 1)?

A. X13 + X23 − .95 X35 − .90 X36 − .90 X37 = 0

B. .80 X13 + .95 X23 − X35 − X36 − X37 = 0

C. .80 X13 + .95 X23 − .90 X36 − .90 X37 ≥ 0

D. X13 + X23 − X35 − X36 − X37 ≥ 0

Question 12

An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 24. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network depicts this problem. What is the balance of flow constraint for node 7 (Diesel)?

A. X35 + X36 + X37 = 75

B. X37 + X47 ≥ 75

C. .90 X37 + .95 X47 = 75

D. X37 + X47 −X36 − X35 − X45 − X46 ≥ 75

Question 13

A network flow problem that allows gains or losses along the arcs is called a

A. nonconstant network flow model.

B. nondirectional, shortest path model.

C. generalized network flow model.

D. transshipment model with linear side constraints.

Question 14

What is the objective function for the following shortest path problem?

Question 15

What happens to the solution of a network flow model if side constraints are added that do not obey the balance of flow rules?

A. The model solution is not guaranteed to be integer.

B. The model solution will more accurately reflect reality.

C. The model solution will be integer but more accurate.

D. The model solution is not guaranteed to be feasible.

Question 16

Consider modeling a warehouse with three inflow arcs and three outflow arcs. The warehouse node is a transshipment node but has a capacity of 100. How would one modify the network model to avoid adding a side constraint that limits either the sum of inflows or the sum of the outflows to 100?

Question 17

The equipment replacement problem is an example of which network problem?

A. transportation problem.

B. shortest path problem.

C. maximal flow problem.

D. minimal spanning tree problem.

Question 18

What is the objective function in the following maximal flow problem?

A. MIN X41

B. MAX X12 + X13

C. MAX X14

D. MAX X41

Question 19

What is the constraint for node 2 in the following maximal flow problem?

A. X12 − X23 − X24 = 0

B. X12 + X23 + X24 = 0

C. X12 ≤ 4

D. X12 + X13 − X23 = 0

Question 20

For a network with n nodes, a spanning tree is

A. a set of (n1) arcs that connects all nodes and contains no loops

B. a set of dummy arcs

C. a set of n arcs that connects all nodes

D. a random subset of arcs covering all nodes

Question 21

One approach to solving integer programming problems is to ignore the integrality conditions and solve the problem with continuous decision variables. This is referred to as

A. quickest solution method.

B. LP satisficing.

C. LP relaxation.

D. LP approximation.

Question 22

The objective function value for the ILP problem can never

A. be as good as the optimal solution to its LP relaxation.

B. be as poor as the optimal solution to its LP relaxation.

C. be worse than the optimal solution to its LP relaxation.

D. be better than the optimal solution to its LP relaxation.

Question 23

Which of the following are potential pitfalls of using a nonzero integer tolerance factor in the Analytic Solver Platform?

A. No assurance the returned solution is optimal.

B. No assurance the returned solution is integer.

C. The true optimal solution may be worse than the returned solution.

D. There are no pitfalls to consider since the Solver will obtain solutions quicker.

Question 24

Which of the following is not a benefit of using binary variables?

A. With only 2 values, Solver can work faster.

B. Binary variables are useful in selection problems.

C. Binary variables can replace some IF() conditions.

D. Binary variables can enforce logical conditions.

Question 25

How are binary variables specified in the Analytic Solver Platform (ASP)?

Question 26

A company wants to select no more than 2 projects from a set of 4 possible projects. Which of the following constraints ensures that no more than 2 will be selected?

Question 27

A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 will be selected?

Question 28

A production company wants to ensure that if Product 1 is produced, production of Product 1 does not exceed production of Product 2. Which of the following constraints enforce this condition?

Question 29

A company must invest in project 1 in order to invest in project 2. Which of the following constraints ensures that project 1 will be chosen if project 2 is invested in?

Question 30

If a company selects Project 1 then it must also select either Project 2 or Project 3 (or both). Which of the following constraints enforces this condition?

Question 31

The setup cost incurred in preparing a machine to produce a batch of product is an example of a A. fixed charge.

Question 32

A manufacturing company has costs associated with production preparation and with per unit production. The per unit production costs are referred to as

Question 33

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below.

Question 34

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below.

Question 35

A company is planning next month’s production. It has to pay a setup cost to produce a batch of X4 ‘s so if it does produce a batch it wants to produce at least 100 units. Which of the following pairs of constraints show the relationship(s) between the setup variable Y4 and the production quantity variable X4?

Question 36

A company will be able to obtain a quantity discount on component parts for its three products, X1 , X2 and X3

if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1 ‘s. It must produce more

than 60 X2 ‘s for the X2 discount and 70 X3 ‘s for the X3 discount. How many binary variables are required in the formulation of this problem?

Question 37

A company will be able to obtain a quantity discount on component parts for its three products, X1 , X2 and X3

if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1 ‘s. It must produce more

than 60 X2 ‘s for the X2 discount and 70 X3’s for the X3 discount. How many decision variables (normal and binary) are required in the formulation of this problem?

Question 38

A company will be able to obtain a quantity discount on component parts for its three products, X1 , X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1 ‘s. It must produce more

Question 39

Suppose you want to minimize an objective function z = 2×1+3×2 . Both decision variables must be integer. The optimal solution to the LP relaxation will:

Question 40

ILP problems are computationally

**BIT 3434 Virginia Tech Quiz**

**Test 3 Questions**

Question 1

For maximization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?

Question 2

For minimization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function

Question 3

In the B & B algorithm, B & B stands for

A. Brooks and Baker

B. Best Bound

C. Best Branch

D. Branch and Bound

Question 4

The B & B algorithm solves ILP problems

A. by solving for each variable separately.

B. by solving for the integer variables first.

C. by solving a series of LP problems.

D. by solving smaller ILP problems.

Question 5

Given the integer model to be solved by BranchandBound

Question 6

For question 5, what would be the starting lower bound solution?

Question 7

For question 5, what would be your first branching constraints?

Question 8

For question 5, what is the final optimal solution?

A. X1 = 0, X2 = 2

B. X1 = 1, X2 = 2

C. X1 = 2, X2 = 1

D. X1 = 2, X2 = 2

E. None of the above

Question 9

A constraint which cannot be violated is called a

A. binding constraint.

B. hard constraint.

C. definite constraint.

D. required constraint.

Question 10

Suppose that X1 equals 4. What are the values for d1 + and d1 in the following constraint?

Question 11

Suppose that the first goal in a GP problem is to make 5 X1 + 7 X2 approximately equal to 50. Using the deviational variables d1

and d1 + , what constraint can be used to express this goal?

Question 12

Suppose that the first goal in a GP problem is to make 3 X1 + 4 X2 approximately equal to 36. Using the deviational variables d1

and d1 +, the following constraint can be used to express this goal.

Question 13

What is the soft constraint form of the following hard constraint?

Question 14

Which of the following formulas is a deviationminimizing objective function for a goal programming problem?

Question 15

What is the meaning of the ti term in this objective function for a goal programming problem?

A. The time required for each decision variable.

B. The percent of goal i met.

C. The coefficient for the ith decision variable

D. The target value for goal i.

Question 16

A manager wants to ensure that he does not exceed his budget by more than $1000 in a goal programming problem. If the budget constraint is the third constraint in the goal programming problem which of the following formulas will best ensure that the manager’s objective is met?

Question 17

The MINIMAX objective

A. yields the smallest possible deviations.

B. minimizes the maximum deviation from any goal.

C. chooses the deviation which has the largest value.

D. maximizes the minimum value of goal attainment.

Question 18

The primary benefit of a MINIMAX objective function is

A. it yields any feasible solution by changing the weights.

B. it is limited to all corner points.

C. it yields a larger variety of solutions than generally available using an LP method.

D. it makes many of the deviational variables equal to zero.

Question 19

A decision maker has expressed concern with Goal 1, budget achievement. She indicated that future candidate solutions should stay under budget. How can you modify your goal programming model to accommodate this change?

Question 20

Goal programming solution feedback indicates that the d4 + level of 50 should not be exceeded in future solution iterations. How should you modify your goal constraint to accommodate this requirement?

Question 21

An investor wants to invest $50,000 in two mutual funds, A and B. The rates of return, risks and minimum investment requirements for each fund are:

Question 22

The main difference between LP and NLP problems is that NLPs will have a

A. linear objective function and nonlinear or linear constraints.

B. minimum of one nonlinear constraint or a nonlinear objective function.

C. multilevel objective functions.

D. multilevel objective function and nonlinear constraints.

Question 23

The optimal solution to a NLP problem can occur at a(n)

Question 24

The GRG and Simplex algorithms are similar in that

A. each algorithm process continues until there is no further improvement in the objective function.

B. both algorithms take their starting solution from the spreadsheet.

C. both return the globally optimal solution.

D. both algorithms return a solution that satisfies at least one constraint at equality.

Question 25

The GRG algorithm operates by

A. moving in the direction of most rapid improvement in the objective function.

B. choosing a search direction at random.

C. searching directly for the optimum solution.

D. moving in a clockwise direction.

Question 26

What is the search path for the following feasible solution space (assuming A is the starting point)? The dashed line represents the objective function and the objective is to maximize the value of the objective function.

Question 27

The GRG algorithm terminates when it

A. has completed 100 iterations.

B. has reached the global optimal solution.

C. detects no feasible direction for improvement.

D. reaches the steepest gradient.

Question 28

Which point or points are local optima in this diagram? The dashed line represents the objective function and the objective is to maximize the value of the objective function.

Question 29

When using the GRG algorithm to solve NLPs one should try multiple starting points because

A. If two different starting points return the same solution, that solution is optimal.

B. the solution returned depends upon the starting point.

C. the solution returned is always near the starting point.

D. a random element of GRG requires multiple starting points.

Question 30

What is the straight line (Euclidean) distance between the points (5,7) and (1,11)?

Question 31

A company has collected the following inventory data for an item. What is the total annual cost for this item?

Annual demand for the item D = 500

Unit purchase cost for the item C = 10

Fixed cost of placing an order S = 20

Cost of holding one unit in inventory for a year i = 30%

Order quantity Q = 50

Question 32

The Reduced Gradient is similar to which of these terms from linear programming?

Question 33

The Lagrange Multiplier is similar to which of these terms from linear programming?

Question 34

In solving the NLP problem, Solver produced a message “Solver found a solution. All constraints and optimality conditions are satisfied.” This means that Solver found:

Question 35

In solving the NLP problem, Solver found a degenerate model. This means that:

Question 36

A company makes products A and B from 2 resources, labor and material. The company wants to determine the selling price which will maximize profits. A unit of product A costs 25 to make and demand is estimated to be 20 −.10 * Price of A. A unit of product B costs 18 to make and demand is estimated to be 30 − .07 * Price of B. The utilization of labor and materials and the available quantity of resources is shown in the table. A reasonable price for the products is between 100 and 200.

Question 37

The global optimum solution to a nonlinear programming problems (NLP), in which the objective function must be minimized, is:

Question 38

The global optimum solution to a nonlinear programming problems (NLP), in which the objective function must be maximized, is:

Question 39

In a genetic algorithm, the random replacement of values in a solution vector is called:

Question 40

The main problem with using Solver and a genetic algorithm to solve a problem is:

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