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.What is the total profit at the optimal solution?
A)$250
B)$398
C)$624
D)$583

Accepted Answer

The optimal solution involves maximizing the use of resources to produce the most profitable combination of shirts and pants. By solving the linear programming problem, the maximum profit is found to be $624.

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.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.Which one of the following corner point (x1,x2)yields the maximum profit in this LP formulation?
A)(24,84)
B)(80,100)
C)(84,24)
D)(80,0)

Accepted Answer

The corner point (24,84) yields the maximum profit because it is the only corner point that satisfies all of the constraints and has the highest objective function value.

Question 3

When the LP problem has more than two decision variables,the ______ is appropriate for searching the optimal solution.
A)graphical method
B)corner point method
C)simplex method
D)iso-profit line method

Accepted Answer

The simplex method is appropriate for finding the optimal solution for LP problems with more than two decision variables. The graphical method is only applicable for problems with two variables, the corner point method may not consider all possible combinations, and the iso-profit line method is not a recognized method in LP.

Question 4

Constraints in LP problems that do not affect the boundaries of the feasible solution region are referred to as ______.
A)redundant constraints
B)binding constraints
C)restrictive constraints
D)optimal constraints

Accepted Answer

Redundant constraints are those which do not contribute to defining any new boundary or edge of the feasible solution space. In other words, they are extra constraints that are already satisfied by other constraints or do not affect the solution space in any way. Therefore, they do not play any role in determining the optimal solution and can be removed from the problem without affecting the feasible solution space or the optimal solution.

Question 5

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.Which one of the following is NOT one of the corner points (x1,x2)in this LP formulation?
A)(24,84)
B)(80,100)
C)(0,100)
D)(80,0)

Accepted Answer

The cutting time constraint is given by 1*X₁ + 1.5*X₂ ≤ 150. To find the corner points, we solve the system of equations given by the constraints. Option B (80,100) would require 80*1 + 100*1.5 = 230 hours of cutting time, which exceeds the maximum of 150 hours available. Therefore, it cannot be a feasible solution or a corner point of the LP formulation.

Question 6

______ are constraints that form the corner points at the boundaries of the feasible solution region and limit the values of the decision variables,which in turn,limit the objective function values.
A)Binding constraints
B)Nonbinding constraints
C)Redundant constraints
D)Optimal constraints

Accepted Answer

Binding constraints are the constraints that limit the feasible solution region and restrict the values of the decision variables. These constraints form the corner points of the feasible solution region and play a crucial role in determining the optimal solution. Nonbinding constraints, on the other hand, do not affect the optimal solution, while redundant constraints are those that do not add any new information and can be eliminated without affecting the problem's solution. Optimal constraints are not a commonly used term in optimization problems.

Question 7

According to the mathematical theory underlying LP problems,the optimal solution to an LP problem will occur at ______.
A)one of the corner points of the feasible space
B)all of the corner points of the feasible space
C)any point inside the feasible space
D)any point outside the feasible space

Accepted Answer

According to the mathematical theory underlying LP problems, the optimal solution to an LP problem will always occur at one of the corner points of the feasible space. This is known as the Corner Point Theorem or the Extreme Point Theorem.

Question 8

For binding constraints at optimality,the right-hand value should be ______ the left-hand value.
A)greater than
B)less than
C)equal to
D)in proportion to

Accepted Answer

For binding constraints, the left-hand side value is equal to the right-hand side value at optimality. This ensures that the constraint is fully satisfied and cannot be relaxed further without violating the feasibility of the problem. Therefore, the right-hand value should be equal to the left-hand value.

Question 9

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.Let X₁ = Number of shirts to be produced,X₂ = Number of pairs of pants to be produced.Determine the value of X₁ and X₂ (that maximizes profit)using corner point method.
A)X₁ = 0,X₂ = 100
B)X₁ = 120,X₂ = 0
C)X₁ = 84,X₂ = 24
D)X₁ = 24,X₂ = 84

Accepted Answer

The answer of ABC,Inc.,is a small clothing manufacturer that produces...

Question 10

Which of the following is a method in which parallel cost lines are plotted in the LP graphical solution approach to determine the least cost solution to LP problems with cost minimization objective?
A)graphical method
B)corner point solution method
C)iso-cost line method
D)iso-profit line method

Accepted Answer

The method described in the question is the iso-cost line method. This involves plotting parallel cost lines on the graph and finding the intersection point that gives the lowest cost solution. Therefore, option C is the correct answer.

Option A, the graphical method, is a broad term that refers to any method that uses graphs to solve LP problems. This includes the iso-cost line method but also includes other methods such as the corner point method.

Option B, the corner point solution method, involves analyzing the corner points of the feasible region to find the optimal solution. It does not involve parallel cost lines, so it is not the best choice in this case.

Option D, the iso-profit line method, is used in LP problems with profit maximization as the objective function. It is not relevant to the cost minimization problem described in the question.

Question 11

Which of the following is an algorithm that provides a systematic way of examining the corner or extreme points of the feasible region of more complex LP problems to determine the optimal value of the objective function?
A)graphical method
B)corner point method
C)simplex method
D)iso-profit line method

Accepted Answer

The simplex method is an algorithm that systematically examines the vertices (or corner points) of the feasible region in linear programming problems to find the optimal value of the objective function. This method is particularly useful for solving more complex LP problems that are not easily solved by graphical methods.

Question 12

In the Excel Solver parameters window,the cell reference for the objective function is an input into which of the following fields?
A)Set Objective
B)By Changing Variable Cells
C)Subject to Constraints
D)Select a Solving Method

Accepted Answer

The cell reference for the objective function is the input for the "Set Objective" field in the Excel Solver parameters window. This field is used to specify the cell that contains the objective function that you want the Solver to optimize.

Question 13

______ is the range of values of the objective function within which the optimal values of the decision variables will not change.
A)Range of feasibility
B)Range of optimality
C)Range of redundancy
D)Range of continuity

Accepted Answer

The range of optimality is the range of values of the objective function within which the optimal values of the decision variables will not change. This means that any value of the objective function within this range will produce the same optimal solution for the decision variables. The range of optimality is important in sensitivity analysis, as it allows us to determine how much the objective function coefficients can change without affecting the optimal solution.

Question 14

At optimality,if the left-hand side values are greater than the right-hand side values,we have ______.
A)slack
B)profit
C)loss
D)surplus

Accepted Answer

At optimality, if the left-hand side values (representing the utilized resources or the value of the decision variables) are greater than the right-hand side values (representing the available resources or constraints), it indicates a surplus situation. This means there are more resources utilized than available, which typically does not align with the standard formulation of linear programming problems but might indicate an issue in the constraint formulation or interpretation.

Question 15

In the Excel Solver parameters window,which of the following options should be selected from the "Select a Solving Method" drop-down menu to solve an LP problem?
A)GRG Onlinear
B)Simplex LP
C)Evolutionary
D)Complex LP

Accepted Answer

Simplex LP is the most appropriate solving method for linear programming problems. GRG Nonlinear, Evolutionary, and Complex LP are intended for nonlinear optimization problems.

Question 16

Which of the following is a method in which parallel profit lines are plotted in the LP graphical solution approach to determine the maximum profit solution to LP problems with profit maximization objective?
A)graphical method
B)corner point solution method
C)iso-cost line method
D)iso-profit line method

Accepted Answer

The method in which parallel profit lines are plotted in the LP graphical solution approach to determine the maximum profit solution to LP problems with profit maximization objective is known as the iso-profit line method. Therefore, option D is the correct answer.

Question 17

At optimality,if the left-hand side values are lesser than the right-hand side values,we have ______.
A)slack
B)profit
C)loss
D)surplus

Accepted Answer

When the left-hand side values are lesser than the right-hand side values at optimality, it means there is still some unused capacity or resources available. This unused capacity is called slack. Therefore, the correct choice is A - slack. Choices B, C, and D are incorrect as they do not accurately describe the situation where the left-hand side values are lesser than the right-hand side values at optimality.

Question 18

The ______ is a process in which each of the corner points occurring at the boundaries of the feasible solution space is examined to determine the optimal solution.
A)graphical method
B)corner point solution method
C)iso-cost line method
D)iso-profit line method

Accepted Answer

The corner point solution method, also known as the corner point optimization method, is used in linear programming to determine the optimal solution by examining each corner point of the feasible solution space. This method involves evaluating the objective function at each corner point to find the maximum or minimum value. Therefore, option B is the correct answer. The graphical method involves plotting the constraints and finding the feasible region, but it does not require examining each corner point. Iso-cost and iso-profit line methods are other techniques used in linear programming to analyze the impact of changes in input and output levels on the costs and profits, respectively.

Question 19

Which of the following methods do we use in conjunction with the corner point method to determine the maximum profit solution to LP problems with profit maximization objective?
A)iso-cost line method
B)sensitivity analysis method
C)simplex method
D)iso-profit line method

Accepted Answer

We use the iso-profit line method in conjunction with the corner point method to determine the maximum profit solution to LP problems with profit maximization objective. The iso-profit line method involves drawing a line representing the objective function value for different profit levels and finding the point where this line intersects with the feasible region. This point corresponds to the maximum profit solution. The other methods mentioned (iso-cost line method, sensitivity analysis method, simplex method) are used in different stages of LP problem-solving but are not specifically used in conjunction with the corner point method for profit maximization.

Question 20

Under instances where the iso-profit line is parallel to one of the constraints that define the boundaries of the feasible solution region,every combination of values of the decision variables that fall on that segment of the constraint line that just touches the feasible solution region is referred to as ______.
A)multiple optimum solutions
B)local optimum solutions
C)global optimum solution
D)single optimum solutions

Accepted Answer

When the iso-profit line is parallel to one of the constraints defining the feasible solution region, it means that the objective function is not affected by changes in that constraint. This leads to multiple points on the constraint line that can provide the same optimal solution, hence multiple optimum solutions.

Quiz 24: Linear Programming

When the LP problem has more than two decision variables,the ______ is appropriate for searching the optimal solution.

Constraints in LP problems that do not affect the boundaries of the feasible solution region are referred to as ______.

______ are constraints that form the corner points at the boundaries of the feasible solution region and limit the values of the decision variables,which in turn,limit the objective function values.

According to the mathematical theory underlying LP problems,the optimal solution to an LP problem will occur at ______.

For binding constraints at optimality,the right-hand value should be ______ the left-hand value.

Which of the following is a method in which parallel cost lines are plotted in the LP graphical solution approach to determine the least cost solution to LP problems with cost minimization objective?

Which of the following is an algorithm that provides a systematic way of examining the corner or extreme points of the feasible region of more complex LP problems to determine the optimal value of the objective function?

In the Excel Solver parameters window,the cell reference for the objective function is an input into which of the following fields?

______ is the range of values of the objective function within which the optimal values of the decision variables will not change.

At optimality,if the left-hand side values are greater than the right-hand side values,we have ______.

In the Excel Solver parameters window,which of the following options should be selected from the "Select a Solving Method" drop-down menu to solve an LP problem?

Which of the following is a method in which parallel profit lines are plotted in the LP graphical solution approach to determine the maximum profit solution to LP problems with profit maximization objective?

At optimality,if the left-hand side values are lesser than the right-hand side values,we have ______.

The ______ is a process in which each of the corner points occurring at the boundaries of the feasible solution space is examined to determine the optimal solution.

Which of the following methods do we use in conjunction with the corner point method to determine the maximum profit solution to LP problems with profit maximization objective?