Question 1

In mathematical programming formulations the objective function may ​contain cubic terms.

Accepted Answer

A) True 
 B)False

Question 2

What most motivates a business to be concerned with efficient use of their resources?

Accepted Answer

A)  Resources are limited and valuable. 
B)  Efficient resource use increases business costs. 
C)  Efficient resources use means more free time. 
D)  Inefficient resource use means hiring more workers.

Question 3

When the objective function can increase without ever contacting a constraint the LP model is said to be

Accepted Answer

A)  infeasible. 
B)  open ended. 
C)  multi-optimal. 
D)  unbounded.

Question 4

What are the three common elements of an optimization problem?

Accepted Answer

A)  objectives, resources, goals. 
B)  decisions, constraints, an objective. 
C)  decision variables, profit levels, costs. 
D)  decisions, resource requirements, a profit function.

Question 5

A production optimization problem has 4 decision variables and a requirement that at least b1 units of material 1 are consumed. Which of the following constraints reflects this fact?

Accepted Answer

A)  f(X1, X2, X3, X4) ≤ b1 
B)  f(X1, X2, X3, X4) ≥ b1 
C)  f(X1, X2, X3, X4) = b1 
D)  f(X1, X2, X3, X4) ≠ b1

Question 6

Bob and Dora Sweet wish to start investing $1,000 each month. The Sweets are looking at five investment plans and wish to maximize their expected return each month. Assume interest rates remain fixed and once their investment plan is selected they do not change their mind. The investment plans offered are:  Since Optima and National are riskier, the Sweets want a limit of 30% per month of their total investments placed in these two investments. Since Safeway and Fidelity are low risk, they want at least 40% of their investment total placed in these investments.
Formulate the LP model for this problem.

Accepted Answer

The answer of Bob and Dora Sweet wish to start...

Question 7

A mathematical programming application employed by a shipping company is most likely

Accepted Answer

A)  a product mix problem. 
B)  a manufacturing problem. 
C)  a routing and logistics problem. 
D)  a financial planning problem.

Question 8

In a mathematical formulation of an optimization problem, the objective function is written as z=2x1+3x2. Then:

Accepted Answer

A)  x1 is a decision variable 
B)  x2 is a parameter 
C)  z needs to be maximized 
D)  2 is a first decision variable level

Question 9

A redundant constraint is one which

Accepted Answer

A)  plays no role in determining the feasible region of the problem. 
B)  is parallel to the level curve. 
C)  is added after the problem is already formulated. 
D)  can only increase the objective function value.

Question 10

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  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?

Accepted Answer

A)  45 
B)  15 
C)  55 
D)  50

Question 11

A facility produces two products and wants to maximize profit. The objective function to maximize is z=350x1+300x2. The number 350 means that:

Accepted Answer

A)  one unit of product 1 contributes $350 to the objective function 
B)  one unit of product 1 contributes $300 to the objective function 
C)  the problem is unbounded 
D)  the problem has no constraints

Question 12

Solve the following LP problem graphically using level curves.

Accepted Answer

The answer of Solve the following LP problem graphically using...

Question 13

Which of the following is the general format of an objective function?

Accepted Answer

A)  f(X1, X2, ..., Xn) ≤ b 
B)  f(X1, X2, ..., Xn) ≥ b 
C)  f(X1, X2, ..., Xn) = b 
D)  f(X1, X2, ..., Xn)

Question 14

A manager has only 200 tons of plastic for his company. This is an example of a(n)

Accepted Answer

A)  decision. 
B)  constraint. 
C)  objective. 
D)  parameter.

Question 15

Most individuals manage their individual retirement accounts (IRAs) so they

Accepted Answer

A)  maximize the amount of money they withdraw. 
B)  minimize the amount of taxes they must pay. 
C)  retire with a minimum amount of money. 
D)  leave all their money to the government.

Question 16

A facility produces two products. The labor constraint (in hours) is formulated as: 350x1+300x2 ≤ 10,000. The number 350 means that

Accepted Answer

A)  one unit of product 1 contributes $350 to the objective function. 
B)  one unit of product 1 uses 350 hours of labor. 
C)  the problem is unbounded. 
D)  the problem has no objective function.

Question 17

The constraints of an LP model define the

Accepted Answer

A)  feasible region 
B)  practical region 
C)  maximal region 
D)  opportunity region

Question 18

What is the goal in optimization?

Accepted Answer

A)  Find the decision variable values that result in the best objective function and satisfy all constraints. 
B)  Find the values of the decision variables that use all available resources. 
C)  Find the values of the decision variables that satisfy all constraints. 
D)  None of these.

Question 19

The following diagram shows the constraints for a LP model. Assume the point (0,0) satisfies constraint (B,J) but does not satisfy constraints (D,H) or (C,I). Which set of points on this diagram defines the feasible solution space? ​  ​

Accepted Answer

A)  A, B, E, F, H 
B)  A, D, G, J 
C)  F, G, H, J 
D)  I, F, G, J

Question 20

Solve the following LP problem graphically using level curves.

Accepted Answer

The answer of Solve the following LP problem graphically using...

Exam 2: Introduction to Optimization and Linear Programming

In mathematical programming formulations the objective function may contain cubic terms.

What most motivates a business to be concerned with efficient use of their resources?

When the objective function can increase without ever contacting a constraint the LP model is said to be

What are the three common elements of an optimization problem?

A production optimization problem has 4 decision variables and a requirement that at least b₁ units of material 1 are consumed. Which of the following constraints reflects this fact?

A mathematical programming application employed by a shipping company is most likely

In a mathematical formulation of an optimization problem, the objective function is written as z=2x₁+3x₂. Then:

A redundant constraint is one which

A facility produces two products and wants to maximize profit. The objective function to maximize is z=350x₁+300x₂. The number 350 means that:

Solve the following LP problem graphically using level curves.

Which of the following is the general format of an objective function?

A manager has only 200 tons of plastic for his company. This is an example of a(n)

Most individuals manage their individual retirement accounts (IRAs) so they

A facility produces two products. The labor constraint (in hours) is formulated as: 350x₁+300x₂ ≤ 10,000. The number 350 means that

The constraints of an LP model define the

What is the goal in optimization?

The following diagram shows the constraints for a LP model. Assume the point (0,0) satisfies constraint (B,J) but does not satisfy constraints (D,H) or (C,I) . Which set of points on this diagram defines the feasible solution space?

Solve the following LP problem graphically using level curves.

Exam 2: Introduction to Optimization and Linear Programming

In mathematical programming formulations the objective function may ​contain cubic terms.

What most motivates a business to be concerned with efficient use of their resources?

When the objective function can increase without ever contacting a constraint the LP model is said to be

What are the three common elements of an optimization problem?

A production optimization problem has 4 decision variables and a requirement that at least b1 units of material 1 are consumed. Which of the following constraints reflects this fact?

A mathematical programming application employed by a shipping company is most likely

In a mathematical formulation of an optimization problem, the objective function is written as z=2x1+3x2. Then:

A redundant constraint is one which

A facility produces two products and wants to maximize profit. The objective function to maximize is z=350x1+300x2. The number 350 means that:

Solve the following LP problem graphically using level curves.

Which of the following is the general format of an objective function?

A manager has only 200 tons of plastic for his company. This is an example of a(n)

Most individuals manage their individual retirement accounts (IRAs) so they

A facility produces two products. The labor constraint (in hours) is formulated as: 350x1+300x2 ≤ 10,000. The number 350 means that

The constraints of an LP model define the

What is the goal in optimization?

The following diagram shows the constraints for a LP model. Assume the point (0,0) satisfies constraint (B,J) but does not satisfy constraints (D,H) or (C,I) . Which set of points on this diagram defines the feasible solution space? ​ ​

Solve the following LP problem graphically using level curves.

In mathematical programming formulations the objective function may contain cubic terms.

A production optimization problem has 4 decision variables and a requirement that at least b₁ units of material 1 are consumed. Which of the following constraints reflects this fact?

In a mathematical formulation of an optimization problem, the objective function is written as z=2x₁+3x₂. Then:

A facility produces two products and wants to maximize profit. The objective function to maximize is z=350x₁+300x₂. The number 350 means that:

A facility produces two products. The labor constraint (in hours) is formulated as: 350x₁+300x₂ ≤ 10,000. The number 350 means that

The following diagram shows the constraints for a LP model. Assume the point (0,0) satisfies constraint (B,J) but does not satisfy constraints (D,H) or (C,I) . Which set of points on this diagram defines the feasible solution space?