Question 1

The third step in formulating a linear programming problem is

Accepted Answer

The answer of The third step in formulating a linear...

Question 2

For an infeasible problem, the feasible region:

Accepted Answer

An infeasible problem is one where no feasible solution exists. Therefore, the feasible region is an empty set.

Question 3

The constraint for resource 1 is 5 X₁ + 4 X₂ ≥ 200. If X₁ = 40 and X₂ = 20, how many additional units, if any, of resource 1 are employed above the minimum of 200?

Accepted Answer

The answer of The constraint for resource 1 is 5...

Question 4

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

Accepted Answer

The number 350 represents the labor hours required for producing one unit of product 1. Since the labor constraint is in terms of labor hours, it makes sense that the coefficient for labor hours (350) is included in the constraint equation.

Question 5

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

Accepted Answer

If there is no way to simultaneously satisfy all the constraints in an LP model, then the problem is infeasible. This means that there is no feasible solution that satisfies all the constraints. The other options (open ended, multi-optimal, unbounded) describe situations where a feasible solution exists, but they do not apply to an LP problem that is infeasible.

Question 6

Mathematical programming is referred to as

Accepted Answer

Mathematical programming is the process of optimizing a function subject to constraints. Hence, A) optimization is the correct choice. Satisficing refers to finding a solution that is satisfactory but not necessarily optimal, C) approximation involves estimating the value of a function or an equation, and D) simulation refers to creating a model of a real-world system and running various scenarios to analyze its behavior.

Question 7

The symbols X₁, Z₁, Dog are all examples of

Accepted Answer

These symbols represent decision variables, which are the variables that decision-makers will choose values for in order to achieve the best outcome in a mathematical model or optimization problem. Constraints and objectives are parts of the model that describe the limitations and goals, respectively, while parameters are constants in the model.

Question 8

This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem? ​  ​

Accepted Answer

The answer of This graph shows the feasible region (defined...

Question 9

The first step in formulating a linear programming problem is

Accepted Answer

Understanding the problem is the initial step in formulating a linear programming problem, as it provides the context and requirements needed to define decision variables, constraints, and the objective function.

Question 10

The number of units to ship from Chicago to Memphis is an example of a(n)

Accepted Answer

The number of units to ship from one location to another is a decision that needs to be made in the context of logistics and supply chain management, making it an example of a decision.

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

The coefficient 350 represents the contribution of one unit of product 1 (S1U1B1) to the objective function. Therefore, choice A is correct. Choice B is incorrect because 300 is the coefficient for the second product in the objective function. Choice C is irrelevant because the information given does not imply an unbounded problem. Choice D is incorrect because the problem is stated to have an objective function to maximize, which indicates constraints are present.

Question 12

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 much profit is earned if the company produces 10 units of product 1 and 5 units of product 2?

Accepted Answer

Based on the given linear programming problem, the profit earned per unit of product 1 is $250 and the profit earned per unit of product 2 is $500. Therefore, if the company produces 10 units of product 1 and 5 units of product 2, the total profit earned will be 10*$250 + 5*$500 = $2750. Hence, the answer is C.

Question 13

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

Accepted Answer

The fact that the manager has only 200 tons of plastic to work with is a limiting factor or constraint. It will impact the decisions he will make, the objectives he can set, and the parameters within which he must operate.

Question 14

What is the goal in optimization?

Accepted Answer

The goal in optimization is to find the values of decision variables that result in the best objective function while also satisfying all constraints. Option A clearly states the goal of optimization. Option B is incorrect as using all available resources may not always result in the best objective function. Option C is too general and does not mention the objective function, which is the primary focus of optimization. Option D is incorrect as there is a goal in optimization.

Question 15

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

The answer of The following diagram shows the constraints for...

Question 16

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

Accepted Answer

Most individuals manage their IRAs to minimize the amount of taxes they must pay. This is because IRAs provide tax benefits, and individuals want to take advantage of those benefits to lower their overall tax burden.

Question 17

Which of the following actions would expand the feasible region of an LP model?

Accepted Answer

Loosening the constraints of an LP model expands the feasible region by allowing more solutions to satisfy the constraints. Tightening constraints, multiplying constraints by a factor, or adding additional constraints generally reduces or alters the feasible region without necessarily expanding it.

Question 18

A linear formulation means that:

Accepted Answer

A linear formulation requires both the objective function and all constraints to be linear. This means that they must involve only the first power of the decision variables, with no multiplication or division between them. All linear programming problems must be specified in this way in order to be solved using standard methods.

Question 19

What are the three common elements of an optimization problem?

Accepted Answer

The three common elements of an optimization problem are decisions, constraints, and an objective. Decision variables are the choices to be made in the optimization problem, constraints are limitations or restrictions on those choices, and the objective is the goal or target that the optimization problem is trying to achieve. Option A is not accurate as goals and objectives are the same thing. Option C is incorrect as profit levels and costs are specific to certain optimization problems and not common to all. Option D is incorrect as resource requirements can be considered as constraints.

Question 20

If constraints are added to an LP model the feasible solution space will generally

Accepted Answer

Constraints limit the feasible solution space by identifying conditions that must be satisfied by any solution. Therefore, adding constraints will generally decrease the feasible solution space.

Quiz 2: Introduction to Optimization and Linear Programming

The third step in formulating a linear programming problem is

For an infeasible problem, the feasible region:

The constraint for resource 1 is 5 X₁ + 4 X₂ ≥ 200. If X₁ = 40 and X₂ = 20, how many additional units, if any, of resource 1 are employed above the minimum of 200?

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

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

Mathematical programming is referred to as

The symbols X₁, Z₁, Dog are all examples of

This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem?

The first step in formulating a linear programming problem is

The number of units to ship from Chicago to Memphis is an example of a(n)

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

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?

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

Which of the following actions would expand the feasible region of an LP model?

A linear formulation means that:

What are the three common elements of an optimization problem?

If constraints are added to an LP model the feasible solution space will generally

Quiz 2: Introduction to Optimization and Linear Programming

The third step in formulating a linear programming problem is

For an infeasible problem, the feasible region:

The constraint for resource 1 is 5 X1 + 4 X2 ≥ 200. If X1 = 40 and X2 = 20, how many additional units, if any, of resource 1 are employed above the minimum of 200?

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

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

Mathematical programming is referred to as

The symbols X1, Z1, Dog are all examples of

This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem? ​ ​

The first step in formulating a linear programming problem is

The number of units to ship from Chicago to Memphis is an example of a(n)

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

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? ​ ​

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

Which of the following actions would expand the feasible region of an LP model?

A linear formulation means that:

What are the three common elements of an optimization problem?

If constraints are added to an LP model the feasible solution space will generally

The constraint for resource 1 is 5 X₁ + 4 X₂ ≥ 200. If X₁ = 40 and X₂ = 20, how many additional units, if any, of resource 1 are employed above the minimum of 200?

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

The symbols X₁, Z₁, Dog are all examples of

This graph shows the feasible region (defined by points ACDEF) and objective function level curve (BG) for a maximization problem. Which point corresponds to the optimal solution to the problem?

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