Question 1

What does LP stand for?

Accepted Answer

LP stands for Linear Program, which is a mathematical optimization problem with linear constraints and a linear objective function.

Question 2

Consider the following three functions: F(x) = 6x² G(x, y) =4x - 3y + 19 H(x, y) = 3xy Which of the following is true regarding the linearity of the functions?

Accepted Answer

G(x, y) = 4x - 3y + 19 is linear because it can be written in the form Ax + By + C, which defines a plane in three-dimensional space. F(x) = 6x^12 is not linear because it involves an exponent on the variable (x^12), which makes it a polynomial of degree 12, not a linear function. H(x, y) = 3xy is not linear because it involves the product of two variables, which makes it a nonlinear function.

Question 3

The algebraic formulation of an optimization problem must state what three things?

Accepted Answer

The three things that must be stated in an algebraic formulation of an optimization problem are decision variables, objective function, and constraints. The decision variables are the variables we can control to optimize the objective function, the objective function is the quantity we want to optimize, and the constraints are the limitations or requirements we must satisfy while optimizing the objective function. Random variables and parameters may be used in the problem, but they do not need to be explicitly stated in the algebraic formulation. Therefore, choice E is the best option.

Question 4

Which type of constraint does not allow the solution for a decision variable of an optimization problem to be less than zero?

Accepted Answer

The constraint type that does not allow the solution for a decision variable of an optimization problem to be less than zero is non-negativity. This means that the decision variable must be equal to or greater than zero. The constraint is often written as x >=0, where x is the decision variable. Therefore, the best choice is (E) non-negativity.

Question 5

If a firm is using a linear program to determine production amounts of its chairs and tables, which of the following constraints must be in the model?

Accepted Answer

Non-negativity constraints are essential in linear programming to ensure that production amounts are not negative.

Question 6

If C represents the number of chairs produced, which of the following is a proper non-negativity constraint?

Accepted Answer

Non-negativity constraints in optimization problems allow variables to be zero or positive, making C ≥ 0 the correct choice.

Question 7

A mathematical model in which one is trying to maximize or minimize some quantity while satisfying a set of constraints is a(n):

Accepted Answer

The definition given in the question fits best with option C, which is a constrained optimization problem. Objective model (A) and decision model (D) are more general terms that can refer to a variety of mathematical models. Constrained model (B) and excel model (E) are not specific enough to describe the optimization problem described in the question.

Question 8

In Linear Programming models, what do you want to do with the objective?

Accepted Answer

In Linear Programming models, the objective is to either maximize or minimize a certain outcome, such as profit or cost, while still satisfying all constraints. Therefore, the objective is to optimize the solution by either maximizing or minimizing the objective function.

Question 9

In Linear Programming models, over what quantities do you have control?

Accepted Answer

In linear programming models, decision variables represent the quantities over which the decision maker has control and can make decisions to optimize. Parameters, constraints, objective variables, and coefficients are all predetermined and cannot be directly controlled by the decision maker.

Question 10

A ____________________ contains explicit definitions of the decision variables, an algebraic expression of the objective function, and algebraic statements of the constraints.

Accepted Answer

The given description matches the definition of a mathematical programming model formulation.

Question 11

Suppose that a firm makes gears (G) and axles (A). Each gear requires 15 minutes of labor and each axle requires 30 minutes of labor. One thousand hours of labor are available. How should the labor constraint(s) be written?

Accepted Answer

To represent the labor constraint(s), we need to find a formula that relates the amount of labor required to produce gears and axles to the total amount of available labor. Using the information given in the problem, we know that each gear requires 15 minutes of labor, and each axle requires 30 minutes of labor. Let G be the number of gears produced and A be the number of axles produced. Then the total amount of labor required can be written as:

Labor required = 15G + 30A

Since we are told that there are 1000 hours of labor available, we can write the constraint as:

15G + 30A ≤ 1000

Dividing both sides of the inequality by 60, we get:

0.25G + 0.5A ≤ 16.67

This is equivalent to choice B, where we have used decimal values instead of fractions. Choice B is the best option since it correctly limits the total amount of labor used by the production of gears and axles.

Question 12

When formulating optimization problems, which of the following represent the typical sequence?

Accepted Answer

The answer of When formulating optimization problems, which of the...

Question 13

Large-scale optimization software can handle how many decision variables and constraints?

Accepted Answer

Modern large-scale optimization software is designed to handle problems of varying sizes, from dozens to millions of decision variables and constraints, making all of these answer choices correct.

Question 14

Testing of the LP model should include __________ and _____________.

Accepted Answer

Testing of the LP model should include the base case and test values. The base case is used to test the model against a known solution, while test values are used to evaluate the model's performance under different conditions. Extreme cases and minimum/maximum values may also be used for testing, but they are not the best choices because they may not provide a realistic evaluation of the model's performance.

Question 15

Once you've written the algebraic formulation of the problem, the next setup involved in Solving Optimization Problems is:

Accepted Answer

The next setup involved in solving optimization problems is to set up the Solver settings. This allows for the optimization algorithm to be applied and the problem to be solved using mathematical techniques. Once the Solver settings have been established, the algorithm can be run and the results can be analyzed and interpreted. Developing test cases and making corrections occur throughout the process, and writing the problem formulation should have already been completed at this point.

Question 16

The text-based formulation of an optimization problem should state what three things?

Accepted Answer

The text-based formulation of an optimization problem should state the decision variables, the objective function that needs to be maximized or minimized, and the constraints on the decision variables that need to be satisfied. Option A is incorrect because random variables are not usually part of optimization problems. Option C is incorrect because random variables are not usually part of optimization problems. Option D is incorrect because random variables are not usually part of optimization problems. Option E is incorrect because parameters are not necessary to state explicitly in the text formulation of an optimization problem.

Question 17

A diagram of the situation can help _______ the problem as well as be a(n) ______ _______ tool.

Accepted Answer

A diagram can help in structuring the problem visually and also be used as a valuable communication tool to convey the information effectively.

Question 18

Human intelligence is not needed in which of the following steps of solving optimization problems?

Accepted Answer

Human intelligence is not required for solving the problem once it has been properly formulated and set up, as this step can be performed by computers or algorithms designed for optimization.

Question 19

What are the allowable constraint relationship types in optimization problems?

Accepted Answer

In optimization problems, constraints are typically expressed using equality (=) and inequality (≤, ≥) relationships.

Question 20

How can the following Linear Program be characterized?
Min X + Y
Subject to
X ≤ 20
Y ≤ 5
X + Y ≥ 40
X, Y ≥ 0

Accepted Answer

The feasible region of this linear program is a triangle with vertices at (0, 5), (20, 20), and (40, 0). Since the objective function is to minimize X + Y, the optimal solution occurs at one of these vertices. However, none of the vertices satisfy the constraint X + Y ≥ 40, which means that the linear program is infeasible. Therefore, the correct choice is (C) bounded and infeasible.

Quiz 18: Introduction to Optimization

What does LP stand for?

Consider the following three functions: F(x) = 6x² G(x, y) =4x - 3y + 19 H(x, y) = 3xy Which of the following is true regarding the linearity of the functions?

The algebraic formulation of an optimization problem must state what three things?

Which type of constraint does not allow the solution for a decision variable of an optimization problem to be less than zero?

If a firm is using a linear program to determine production amounts of its chairs and tables, which of the following constraints must be in the model?

If C represents the number of chairs produced, which of the following is a proper non-negativity constraint?

A mathematical model in which one is trying to maximize or minimize some quantity while satisfying a set of constraints is a(n) :

In Linear Programming models, what do you want to do with the objective?

In Linear Programming models, over what quantities do you have control?

A ____________________ contains explicit definitions of the decision variables, an algebraic expression of the objective function, and algebraic statements of the constraints.

Suppose that a firm makes gears (G) and axles (A) . Each gear requires 15 minutes of labor and each axle requires 30 minutes of labor. One thousand hours of labor are available. How should the labor constraint(s) be written?

When formulating optimization problems, which of the following represent the typical sequence?

Large-scale optimization software can handle how many decision variables and constraints?

Testing of the LP model should include and ___.

Once you've written the algebraic formulation of the problem, the next setup involved in Solving Optimization Problems is:

The text-based formulation of an optimization problem should state what three things?

A diagram of the situation can help _ the problem as well as be a(n) ___ tool.

Human intelligence is not needed in which of the following steps of solving optimization problems?

What are the allowable constraint relationship types in optimization problems?

How can the following Linear Program be characterized? Min X + Y Subject to X ≤ 20 Y ≤ 5 X + Y ≥ 40 X, Y ≥ 0

Quiz 18: Introduction to Optimization

What does LP stand for?

Consider the following three functions: F(x) = 6x2 G(x, y) =4x - 3y + 19 H(x, y) = 3xy Which of the following is true regarding the linearity of the functions?

The algebraic formulation of an optimization problem must state what three things?

Which type of constraint does not allow the solution for a decision variable of an optimization problem to be less than zero?

If a firm is using a linear program to determine production amounts of its chairs and tables, which of the following constraints must be in the model?

If C represents the number of chairs produced, which of the following is a proper non-negativity constraint?

A mathematical model in which one is trying to maximize or minimize some quantity while satisfying a set of constraints is a(n) :

In Linear Programming models, what do you want to do with the objective?

In Linear Programming models, over what quantities do you have control?

A ____________________ contains explicit definitions of the decision variables, an algebraic expression of the objective function, and algebraic statements of the constraints.

Suppose that a firm makes gears (G) and axles (A) . Each gear requires 15 minutes of labor and each axle requires 30 minutes of labor. One thousand hours of labor are available. How should the labor constraint(s) be written?

When formulating optimization problems, which of the following represent the typical sequence?

Large-scale optimization software can handle how many decision variables and constraints?

Testing of the LP model should include __________ and _____________.

Once you've written the algebraic formulation of the problem, the next setup involved in Solving Optimization Problems is:

The text-based formulation of an optimization problem should state what three things?

A diagram of the situation can help _______ the problem as well as be a(n) ______ _______ tool.

Human intelligence is not needed in which of the following steps of solving optimization problems?

What are the allowable constraint relationship types in optimization problems?

How can the following Linear Program be characterized? Min X + Y Subject to X ≤ 20 Y ≤ 5 X + Y ≥ 40 X, Y ≥ 0

Consider the following three functions: F(x) = 6x² G(x, y) =4x - 3y + 19 H(x, y) = 3xy Which of the following is true regarding the linearity of the functions?

Testing of the LP model should include and ___.

A diagram of the situation can help _ the problem as well as be a(n) ___ tool.