Question 1

Identify three examples of resources that are typically constrained in a linear programming problem.

Accepted Answer

The textbook gives machinery,labor,money,time,and raw materials.

Question 2

Which of the following is not a requirement of a linear programming problem?
A)an objective function,expressed in linear terms
B)constraints,expressed as linear equations or inequalities
C)an objective function to be maximized or minimized
D)alternative courses of action
E)one constraint or resource limit for each decision variable

Accepted Answer

E

Question 3

One requirement of a linear programming problem is that the objective function must be expressed as a linear equation.

Accepted Answer

Linear programming is a mathematical technique used to optimize a linear objective function subject to a set of linear constraints. The objective function must be a linear equation in order to be maximized or minimized using linear programming.

Question 4

In which of the following has LP been applied successfully?
A)minimizing distance traveled by school buses carrying children
B)minimizing 911 response time for police patrols
C)minimizing labor costs for bank tellers while maintaining service levels
D)determining the distribution system for multiple warehouses to multiple destinations
E)all of the above

Accepted Answer

Linear programming has been used successfully in all of the stated scenarios. It can be used in any situation where there are multiple variables that need to be optimized while adhering to constraints.

Question 5

The ________ is a mathematical expression in linear programming that maximizes or minimizes some quantity.

Accepted Answer

The answer of The ________ is a mathematical expression in...

Question 6

A linear programming problem contains a restriction that reads "the quantity of S must be no less than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.
A)S / (T + U)≥ 4
B)S - .25T -.25U ≥ 0
C)4S ≤ T + U
D)S ≥ 4T / 4U
E)S ≥ .25T + S ≥ .25U

Accepted Answer

To translate the restriction "the quantity of S must be no less than one-fourth as large as T and U combined" to a linear programming constraint, we need to express it as an inequality. 
Let's first express "one-fourth as large as T and U combined" as (T+U)/4. 
The restriction then becomes S ≥ (T+U)/4. 
Multiplying both sides by 4 gives 4S ≥ T+U, which is equivalent to S - 0.25T - 0.25U ≥ 0 after dividing both sides by 4. Therefore, the correct choice is B.

Question 7

________ are restrictions that limit the degree to which a manager can pursue an objective.

Accepted Answer

The answer of ________ are restrictions that limit the degree...

Question 8

A firm makes two products,Y and Z.Each unit of Y costs $10 and sells for $40.Each unit of Z costs $5 and sells for $25.If the firm's goal were to maximize profit,what would be the appropriate objective function?
A)Maximize profit = $40Y = $25Z
B)Maximize profit = $40Y + $25Z
C)Maximize profit = $30Y + $20Z
D)Maximize profit = 0.25Y + 0.20Z
E)Maximize profit = $50(Y + Z)

Accepted Answer

The correct objective function to maximize profit is to calculate the profit per unit for each product and then sum these profits. For product Y, the profit per unit is $40 (selling price) - $10 (cost) = $30. For product Z, the profit per unit is $25 (selling price) - $5 (cost) = $20. Therefore, the objective function is to maximize $30Y + $20Z.

Question 9

What are the requirements of all linear programming problems?

Accepted Answer

The answer of What are the requirements of all linear...

Question 10

Which of the following represents a valid constraint in linear programming?
A)2X ≥ 7XY
B)(2X)(7Y)≥ 500
C)2X + 7Y ≥100
D)2X2 + 7Y ≥ 50
E)All of the above are valid linear programming constraints.

Accepted Answer

A valid constraint in linear programming must be a linear equation, meaning it cannot have any exponents or products of variables. Option C is the only linear equation out of the given options and therefore the valid constraint.

Question 11

A linear programming problem contains a restriction that reads "the quantity of Q must be no larger than the sum of R,S,and T." Formulate this as a linear programming constraint.
A)Q + R + S + T ≤ 4
B)Q ≥ R + S + T
C)Q - R - S - T ≤ 0
D)Q / (R + S + T)≤ 0
E)Q ≤ R + Q ≤ S + Q ≤ T

Accepted Answer

The restriction "the quantity of Q must be no larger than the sum of R, S, and T" can be written as Q ≤ R + S + T. To write this in the standard form of a linear programming constraint, we simply move all the variables to one side: Q - R - S - T ≤ 0. This is option C.

Question 12

________ is a mathematical technique designed to help operations managers plan and make decisions necessary to allocate resources.

Accepted Answer

The answer of ________ is a mathematical technique designed to...

Question 13

A linear programming problem contains a restriction that reads "the quantity of X must be at least three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?
A)3X ≥ Y
B)X ≤ 3Y
C)X + Y ≥ 3
D)X - 3Y ≥ 0
E)3X ≤ Y

Accepted Answer

The answer of A linear programming problem contains a restriction...

Question 14

In a linear programming formulation,a statement such as "maximize contribution" becomes a(n):
A)constraint.
B)slack variable.
C)objective function.
D)violation of linearity.
E)decision variable.

Accepted Answer

In linear programming, the objective function is the function that is to be maximized or minimized. In this case, the objective is to maximize the contribution, so it becomes the objective function in the formulation.

Question 15

Linear programming is an appropriate problem-solving technique for decisions that have no alternative courses of action.

Accepted Answer

Linear programming is a problem-solving technique for optimizing a linear objective function subject to linear constraints. It is used for decisions with alternative courses of action that can be mathematically modeled.

Question 16

In linear programming,a statement such as "maximize contribution" becomes an objective function when the problem is formulated.

Accepted Answer

This statement can be transformed into an objective function by assigning a variable to the contribution and maximizing that variable. Therefore, it is true that "maximize contribution" becomes an objective function in linear programming.

Question 17

The requirements of linear programming problems include an objective function,the presence of constraints,objective and constraints expressed in linear equalities or inequalities,and ________.

Accepted Answer

The answer of The requirements of linear programming problems include...

Question 18

Linear programming helps operations managers make decisions necessary to make effective use of resources such as machinery,labor,money,time,and raw materials.

Accepted Answer

Linear programming is a mathematical technique used to optimize the allocation of limited resources to achieve a set of objectives or constraints. It is commonly used in operations management to make decisions on how to best use resources such as machinery, labor, money, time, and raw materials. Therefore, the statement is true.

Question 19

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

Accepted Answer

This statement accurately describes the product-mix problem in linear programming.

Question 20

What is linear programming?

Accepted Answer

The answer of What is linear programming?...

Quiz 23: Linear Programming

Identify three examples of resources that are typically constrained in a linear programming problem.

Which of the following is not a requirement of a linear programming problem?

One requirement of a linear programming problem is that the objective function must be expressed as a linear equation.

In which of the following has LP been applied successfully?

The ________ is a mathematical expression in linear programming that maximizes or minimizes some quantity.

A linear programming problem contains a restriction that reads "the quantity of S must be no less than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.

________ are restrictions that limit the degree to which a manager can pursue an objective.

A firm makes two products,Y and Z.Each unit of Y costs $10 and sells for $40.Each unit of Z costs $5 and sells for $25.If the firm's goal were to maximize profit,what would be the appropriate objective function?

What are the requirements of all linear programming problems?

Which of the following represents a valid constraint in linear programming?

A linear programming problem contains a restriction that reads "the quantity of Q must be no larger than the sum of R,S,and T." Formulate this as a linear programming constraint.