Question 1

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

Accepted Answer

The objective function in a linear programming problem must be expressed as a linear equation or inequality in order for the problem to be considered a linear programming problem.

Question 2

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.

Accepted Answer

The restriction can be written as Q <= R + S + T. Since we want all variables on the left-hand side, we can also write this as Q - R - S - T <= 0. This is equivalent to the constraint in option C.

Question 3

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 objective of the product-mix linear programming problem.

Question 4

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

This statement is true. Linear programming is a mathematical technique used to optimize the use of limited resources in order to achieve a specific objective, such as maximizing profits or minimizing costs. This makes it a useful tool for operations managers who need to balance multiple factors in order to make informed decisions about how to allocate resources.

Question 5

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

Accepted Answer

A valid linear programming constraint must be linear, meaning that it cannot include nonlinear terms such as XY or X^2. Constraint C is linear and fits the form Ax + By ≥ C, where A, B, and C are constants and x and y are variables. Therefore, constraint C is a valid choice for linear programming.

Question 6

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

Accepted Answer

The answer of Identify three examples of resources that are...

Question 7

In a linear programming formulation,a statement such as "maximize contribution" becomes a(n):

Accepted Answer

"Maximize contribution" is the goal or objective of the linear programming problem, so it becomes the objective function.

Question 8

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

Accepted Answer

Linear programming involves finding the optimal solution among multiple feasible alternatives, which means there are alternative courses of action to consider. Therefore, this statement is false.

Question 9

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

Accepted Answer

In linear programming, the objective function is a mathematical expression that represents the quantity to be optimized, such as maximizing profit, minimizing costs, or, as in this case, maximizing contribution.

Question 10

What is linear programming?

Accepted Answer

The answer of What is linear programming?...

Question 11

________ 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 12

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?

Accepted Answer

The constraint "the quantity of X must be at least three times as large as the quantity of Y" translates to X being greater than or equal to 3 times Y, which is expressed as X - 3Y ≥ 0.

Question 13

________ 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 14

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.

Accepted Answer

The restriction can be written as S ≥ 0.25(T+U), which can be rearranged as S - 0.25T - 0.25U ≥ 0. This is the same as option B. Option A is incorrect because it has the inequality sign in the wrong direction. Option C is incorrect because it has the constant on the wrong side of the inequality sign. Option D is incorrect because it has a faulty equation that says S should be greater than both T and U, rather than their sum. Option E is incorrect because it has two separate inequalities instead of one.

Question 15

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 16

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

Accepted Answer

Linear programming problems do not require one constraint or resource limit for each decision variable. Constraints can involve multiple decision variables and are not limited to a one-to-one relationship.

Question 17

What are the requirements of all linear programming problems?

Accepted Answer

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

Question 18

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?

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 19

In which of the following has LP been applied successfully?

Accepted Answer

LP (Linear Programming) has been successfully applied in all of the given scenarios. LP is a mathematical optimization technique that helps in minimizing or maximizing a linear objective function while satisfying a set of linear constraints. In all of the given scenarios, LP can be used to optimize the objective while satisfying the constraints.

Question 20

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...

Quiz 23: Linear Programming