Question 1

ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine the objective function for the LP formulation.
A)Maximize profit = $11 * (Number of shirts to be produced + Number of pairs of pants to be produced)
B)Maximize profit = $5 * Number of shirts to be produced
C)Maximize profit = $6 * Number of pairs of pants to be produced
D)Maximize profit = ($5 * Number of shirts to be produced)+ ($6 * Number of pairs of pants to be produced)

Accepted Answer

The objective function for maximizing profit would be to produce both shirts and pants, as they both generate profits. The objective function would be to maximize profit, which is calculated by adding the profit generated from producing shirts and pants together, making choice D the best option.

Question 2

ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine the nonnegative constraint for the LP formulation.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.
A)X₁ and X₂ > 0
B)X₁ and X₂ ≥ 0
C)X₁ and X₂ ≤ 0
D)X₁ and X₂ = 0

Accepted Answer

The nonnegative constraint means that the values for X₁ and X₂ cannot be negative. It is because it does not make sense to produce a negative number of shirts or pants. Therefore, the correct choice is B, which states that X₁ and X₂ must be greater than or equal to zero.

Question 3

All linear programming problems must have ______ distinct features.
A)three
B)four
C)five
D)six

Accepted Answer

All linear programming problems must have four distinct features: an objective function, decision variables, constraints, and non-negativity constraints.

Question 4

Which of the following is a mathematical modeling technique that managers can use in making decisions that involve optimizing an objective,subject to constraints?
A)optimization
B)estimation
C)linear programming
D)transportation model

Accepted Answer

Linear programming is a mathematical technique that helps managers optimize an objective, subject to constraints. It involves creating a mathematical model of the problem, where an objective function is optimized while considering limitations or constraints. Optimization, estimation, and transportation modeling are related techniques but are not specifically used for this purpose.

Question 5

Determining the supply of resources needed to meet demand for the intermediate time frame at the minimum cost is an example of applying linear programming to solving ______ problems.
A)financial planning
B)production planning
C)assignment
D)transportation

Accepted Answer

Linear programming is commonly used in production planning to optimize the use of resources such as labor, machines, and raw materials. The objective is to find the combination of inputs that will maximize output while minimizing costs.

Question 6

ABC,Inc.,is a small clothing manufacturer that produces polo shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hours cutting machine time.Production of one polo shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each polo shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.How many decision variables are there in this LP formulation?
A)one
B)two
C)three
D)four

Accepted Answer

There are two decision variables: the number of polo shirts produced and the number of pairs of pants produced.

Question 7

In linear programming,advertising dollars budgeted for a marketing campaign is an example of ______.
A)a variable
B)a resource
C)a constraint
D)an objective

Accepted Answer

The answer of In linear programming,advertising dollars budgeted for a...

Question 8

The requirement of linear programming is that the objective function and the constraints have ______ relationship.
A)independent
B)linear
C)exponential
D)nonlinear

Accepted Answer

Linear programming requires that the objective function and constraints have a linear relationship, which means that they can be represented by linear equations or inequalities. This allows for the use of linear algebra and optimization techniques to find the optimal solution. The other options, independent, exponential, and nonlinear, do not meet this requirement.

Question 9

The graphical method is appropriate for solving simple linear programming problems involving ______ decision variables.
A)one
B)two
C)three
D)four

Accepted Answer

The graphical method works well for problems with two decision variables as they can easily be plotted on a two-dimensional coordinate system. For problems with more than two variables, the graphical method becomes more complex and difficult to visualize. Problems with one variable do not generally require the use of linear programming techniques.

Question 10

ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine sewing time constraint for the LP formulation.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.
A)3X₁ + 2X₂ ≤ 240
B)X₁ + 1.5X₂ ≤ 150
C)3X₁ + 2X₂ ≤ 150
D)X₁ + 1.5X₂ ≤ 240

Accepted Answer

The sewing machine hours are the limiting factor in this scenario as there are only 240 hours available. Each shirt takes 3 hours of sewing machine time, and each pair of pants takes 2 hours of sewing machine time. Therefore, the constraint for sewing machine time can be expressed as 3X₁ + 2X₂ ≤ 240, where X₁ is the number of shirts and X₂ is the number of pairs of pants produced.

Question 11

The limited availability of resources can be referred to as ______.
A)constraints
B)variables
C)consequences
D)state of nature

Accepted Answer

The term "constraints" refers to limiting factors or restrictions that affect the availability or use of resources. The other options, "variables" and "state of nature," do not necessarily imply a scarcity of resources, while "consequences" refers to the results or outcomes of a decision or action, rather than the limited availability of resources themselves.

Question 12

The resource constraints are modeled in LP mathematically as ______.
A)inequalities
B)equalities or inequalities
C)linearity
D)variables

Accepted Answer

Resource constraints can be modeled as either equalities or inequalities in LP. Equalities represent a strict limit on the availability of resources, while inequalities represent a more flexible constraint where resources can be exceeded up to a certain point. Choosing both A and C would not be accurate as linearity refers to a property in LP optimization, whereas variables are the unknown quantities being optimized.

Question 13

In linear programming,maximizing profits or minimizing costs is an example of ______.
A)a variable
B)a resource
C)a constraint
D)an objective

Accepted Answer

Maximizing profits or minimizing costs is an objective in linear programming. The objective represents the overarching goal of the optimization problem and is usually stated in terms of maximizing or minimizing a certain quantity, such as profits, production output, or resource usage. Variables are decision variables that we can adjust to achieve the objective, resources are inputs that we can utilize to produce outputs, and constraints are limitations or restrictions on the variables and resources that we have available to us.

Question 14

Which of the following is FALSE about objective functions in linear programming (LP)?
A)Every LP problem will have an objective function.
B)An objective function can be either maximized or minimized.
C)The objective of an LP problem expressed mathematically is referred to as an objective function.
D)The objective for an LP problem should be expressed explicitly in monetary units.

Accepted Answer

The objective of an LP problem does not necessarily need to be expressed explicitly in monetary units. It can be any measurable quantity that needs to be maximized or minimized, such as time, distance, or production volume.

Question 15

Which of the following is NOT one of the features of a linear programming problem?
A)decision variables
B)consequences
C)constraints
D)linearity

Accepted Answer

Consequences are not a feature of linear programming problems. The main features of a linear programming problem are decision variables, constraints, and linearity.

Question 16

______ in linear programming are an alternative course of action-for example,determining the number of shipping routes for transporting goods from the available alternative choices.
A)Decision variables
B)Consequences
C)Constraints
D)Linearity

Accepted Answer

Decision variables in linear programming represent the choices or decisions that must be made in order to achieve the objective, such as how many shipping routes to use. This is in contrast to constraints, which limit the feasible options, and consequences, which are the outcomes of the decisions. Linearity refers to the mathematical relationships between the decision variables, constraints, and objective function. Therefore, the best choice is A) Decision variables.

Question 17

ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hour cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Determine cutting time constraint for the LP formulation.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.
A)3X₁ + 2X₂ ≤ 240
B)X₁ + 1.5X₂ ≤ 150
C)3X₁ + 2X₂ ≤ 150
D)X₁ + 1.5X₂ ≤ 240

Accepted Answer

To determine the cutting time constraint for the LP formulation, we need to find the total amount of cutting time required for the production of X₁ shirts and X₂ pairs of pants.

For X₁ shirts, the cutting time required is X₁ hours (1 hour per shirt).

For X₂ pairs of pants, the cutting time required is 1.5X₂ hours (1.5 hours per pair of pants).

Therefore, the total cutting time required is:

Cutting time = X₁ + 1.5X₂

To maximize profits, we need to ensure that the total cutting time required does not exceed the maximum cutting machine time available, which is 150 hours.

Thus, the cutting time constraint for the LP formulation is:

X₁ + 1.5X₂ ≤ 150

Therefore, the best choice is B.

Question 18

Using linear programming (LP)to determine the optimum investment portfolio that will achieve certain returns while minimizing investment risks is an example of applying LP to solving ______ problems.
A)financial planning
B)production planning
C)assignment
D)transportation

Accepted Answer

Linear programming is widely used in financial planning to optimize the portfolio of investments to achieve certain financial goals, such as maximizing returns while minimizing risks. Therefore, using LP to determine the optimum investment portfolio belongs to financial planning problems. The other options, such as production planning, assignment, and transportation, belong to different categories of problems that can be solved using LP but are not directly related to optimizing investment portfolios.

Question 19

Determining the shipment of goods from multiple sources to multiple destinations to minimize transportation costs is an example of applying linear programming to solving ______ problems.
A)financial planning
B)production planning
C)assignment
D)transportation

Accepted Answer

The given scenario of determining the shipment of goods from multiple sources to multiple destinations to minimize transportation costs is an example of a transportation problem that can be solved using linear programming. Linear programming is a mathematical technique used to optimize solutions for problems like manufacturing, transportation, financial planning, etc. However, in this case, the problem clearly involves transportation, hence option D is the best choice.

Question 20

ABC,Inc.,is a small clothing manufacturer that produces shirts and pants using two resources: sewing machine hours and cutting machine hours.The production manager can schedule up to 240 hours of sewing machine time and up to 150 hours of cutting machine time.Production of one shirt requires 3 hours of sewing time and 1 hour of cutting time.Each pair of pants requires 2 hours of sewing time and 1.5 hours of cutting time.Each shirt yields a profit of $5,and each pair of pants generates a $6 profit.The objective is to maximize profits.Which of the following is the decision variable for the LP formulation?
A)total revenue generated
B)number of sewing hours and number of cutting hours required
C)number of shirts and number of pairs of pants to be produced
D)total production time

Accepted Answer

The decision variables in this LP formulation are the number of shirts and the number of pairs of pants to be produced. These variables are what the production manager has control over and can adjust in order to maximize profits. The other options (total revenue generated, number of sewing hours and number of cutting hours required, and total production time) are either outcomes of the decision variables or constraints on the decision variables.

Quiz 24: Linear Programming

All linear programming problems must have ______ distinct features.

Which of the following is a mathematical modeling technique that managers can use in making decisions that involve optimizing an objective,subject to constraints?

Determining the supply of resources needed to meet demand for the intermediate time frame at the minimum cost is an example of applying linear programming to solving ______ problems.

In linear programming,advertising dollars budgeted for a marketing campaign is an example of ______.

The requirement of linear programming is that the objective function and the constraints have ______ relationship.

The graphical method is appropriate for solving simple linear programming problems involving ______ decision variables.

The limited availability of resources can be referred to as ______.

The resource constraints are modeled in LP mathematically as ______.

In linear programming,maximizing profits or minimizing costs is an example of ______.

Which of the following is FALSE about objective functions in linear programming (LP) ?

Which of the following is NOT one of the features of a linear programming problem?

______ in linear programming are an alternative course of action-for example,determining the number of shipping routes for transporting goods from the available alternative choices.

Using linear programming (LP) to determine the optimum investment portfolio that will achieve certain returns while minimizing investment risks is an example of applying LP to solving ______ problems.

Determining the shipment of goods from multiple sources to multiple destinations to minimize transportation costs is an example of applying linear programming to solving ______ problems.