Question 1

A parameter is a region that represents all permissible combinations of the decision variables in a linear programming model.

Accepted Answer

A parameter is a known constant value in a linear programming model, such as the coefficients of the objective function or the constraints. The region that represents all permissible combinations of the decision variables is called the feasible region.

Question 2

Which of the following statements regarding linear programming is NOT true?
A)A parameter is also known as a decision variable.
B)Linearity assumes proportionality and additivity.
C)The product-mix problem is a one-period type of aggregate planning problem.
D)One reasonable sequence for formulating a model is defining the decision variables,writing out the objective function,and writing out the constraints.

Accepted Answer

A

Question 3

A site manager has three day laborers available for eight hours each and a burning desire to maximize his return on their wages.The site manager uses linear programming to assign them to two tasks and notes that he has enough work to occupy 21 labor hours.The linear program that the site manager has constructed has
A)slack.
B)surplus.
C)a positive shadow price for labor.
D)no feasible solution.

Accepted Answer

D

Question 4

The graphical method is a practical method for solving product mix problems of any size,provided the decision maker has sufficient quantities of graph paper.

Accepted Answer

The graphical method requires graph paper, but it may not be practical for solving product mix problems of large size. Other methods such as linear programming may be more suitable.

Question 5

For the line that has the equation 4X1 + 8X2 = 88,an axis intercept is
A)(0,22).
B)(6,0).
C)(6,22).
D)(0,11).

Accepted Answer

The answer of For the line that has the equation...

Question 6

In linear programming,each parameter is assumed to be known with certainty.

Accepted Answer

Linear programming assumes that all parameters, such as coefficients and constraints, are known with certainty and do not involve any randomness or uncertainty. This is known as deterministic modeling.

Question 7

Linear programming is useful for allocating scarce resources among competing demands.

Accepted Answer

Linear programming is a mathematical technique that is used for optimization. It is designed to help find the best solution or course of action among a set of available alternatives, given a series of constraints or limitations. Therefore, it is useful for allocating scarce resources among competing demands.

Question 8

One assumption of linear programming is that a decision maker cannot use negative quantities of the decision variables.

Accepted Answer

Linear programming models assume that decision makers will not use negative quantities of decision variables. This is because negative values would imply that the decision maker is producing, consuming, or shipping negative quantities, which is not realistic.

Question 9

A binding constraint is the amount by which the left-hand side falls short of the right-hand side.

Accepted Answer

A binding constraint is a condition or limitation that restricts the actions or operations of a system. It is not measured as the difference between two sides of an equation.

Question 10

Only corner points should be considered for the optimal solution to a linear programming problem.

Accepted Answer

This statement is true. In linear programming, the optimal solution occurs at one of the corner points (also known as vertices or extreme points) of the feasible region. This is known as the Corner Point Theorem. Therefore, only the corner points need to be considered in order to obtain the optimal solution.

Question 11

The objective function Maximize Z = 3x2 = 4y is appropriate.

Accepted Answer

The objective function should have a consistent format, such as Maximize Z = 3x + 4y, where Z is expressed as a linear combination of variables x and y.

Question 12

A manager is interested in deciding production quantities for products A,B,and C.He has an inventory of 20 tons each of raw materials 1,2,3,and 4 that are used in the production of products A,B,and C.He can further assume that he can sell all of what he makes.Which of the following statements is correct?
A)The manager has four decision variables.
B)The manager has three constraints.
C)The manager has three decision variables.
D)The manager can solve this problem graphically.

Accepted Answer

The manager has three decision variables because he is deciding production quantities for three products. He has four constraints (one for each raw material inventory). The problem can be solved graphically, but additional information such as the demand and production costs would be needed to fully solve the problem.

Question 13

Consider a corner point to a linear programming problem,which lies at the intersection of the following two constraints: 6X1 + 15X2 < 390 2X1 + X2 < 50 Which of the following statements about the corner point is true? A)X1 < 21 B)X1 > 25 C)X1 < 10 D)X1 > 17

Accepted Answer

The answer of Consider a corner point to a linear...

Question 14

Which of the following statements regarding linear programming is NOT true?
A)A linear programming problem can have more than one optimal solution.
B)Most real-world linear programming problems are solved on a computer.
C)If a binding constraint were relaxed,the optimal solution wouldn't change.
D)A surplus variable is added to a > constraint to convert it to an equality.

Accepted Answer

If a binding constraint were relaxed, the optimal solution may or may not change. Depending on the specific problem, relaxing a binding constraint may result in a new optimal solution or no change to the existing optimal solution.

Question 15

A binding constraint has slack but does not have surplus.

Accepted Answer

A binding constraint does not have slack or surplus because it is exactly met in the solution of a linear programming problem, meaning the resources are fully utilized without any excess or shortfall.

Question 16

Suppose that the optimal values of the decision variables to a two-variable linear programming problem remain the same as long as the slope of the objective function lies between the slopes of the following two constraints: 2X1 + 3X2 < 26
2X1 + 2X2 < 20
The current objective function is:
8X1 + 9X2 = Z
Which of the following statements about the range of optimality on c1 is TRUE?
A)0 < c1 < 2
B)2 < c1 < 6
C)6 < c1 < 9
D)9 < c1 < 12

Accepted Answer

The slope of the objective function (c1/c2) must lie between the slopes of the constraints. The slopes of the constraints are -2/3 and -1. The slope of the current objective function is -8/9. For the optimal solution to remain unchanged, the slope of the objective function must be between -2/3 and -1, which corresponds to 6 < c1 < 9 when c2 is 9.

Question 17

A constraint is a limitation that restricts the permissible choices.

Accepted Answer

A constraint is indeed a limitation that restricts the permissible choices, therefore the statement is true.

Question 18

The simplex method is an interactive algebraic procedure for solving linear programming problems.

Accepted Answer

The statement accurately describes the simplex method.

Question 19

A manager is interested in using linear programming to analyze production for the ensuing week.She knows that it will take exactly 1.5 hours to run a batch of product A and that this batch will consume two tons of sugar.This is an example of the linear programming assumption of
A)linearity.
B)certainty.
C)continuous variables.
D)whole numbers.

Accepted Answer

The assumption of certainty refers to the assumption that all of the input parameters in a linear programming problem are known with complete accuracy. In this case, the manager knows exactly how long it will take to produce a batch of product A and how much sugar it will consume. Therefore, the assumption of certainty is being used. The other options (linearity, continuous variables, and whole numbers) are characteristics of linear programming problems but are not applicable to this specific assumption.

Question 20

Decision variables are represented in both the objective function and the constraints while formulating a linear program.

Accepted Answer

Decision variables are used in the objective function and constraints to represent the quantities or values that the linear program seeks to optimize or satisfy. They are typically denoted by x1, x2, x3...xn and are adjusted by the solver to find the optimal solution.

Quiz 22: Linear Programming