Question 1

Sensitivity analysis of linear programming solutions can use trial and error or the analytic postoptimality method.

Accepted Answer

Sensitivity analysis in linear programming can indeed use both trial and error and the analytic postoptimality method to assess how changes in the parameters (such as coefficients in the objective function or constraints) affect the optimal solution.

Question 2

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

Accepted Answer

This is true, as linear programming problems are designed to optimize linear objective functions.

Question 3

The graphical method of solving linear programming can handle only maximizing problems.

Accepted Answer

The graphical method can handle both maximizing and minimizing problems.

Question 4

For a linear programming problem with the constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, two of its corner points are (0, 0) and (0, 25).

Accepted Answer

The answer of For a linear programming problem with the...

Question 5

The optimal solution of a linear programming problem that consists of two variables and six constraints will probably not satisfy all six constraints as equalities.

Accepted Answer

It is possible for the optimal solution to satisfy all six constraints as equalities, but it is not necessarily the case. In many cases, the optimal solution will satisfy some constraints as strict inequalities, meaning they are not met as equalities. This is because the constraints often create a feasible region that is a convex polygon or polyhedron, and the optimal solution will lie on one of the vertices or edges of this region.

Question 6

Which of the following represents valid constraints in linear programming? A) 2X ≥ 7X × Y B) 2X × 7Y ≥ 500 C) 2X + 7Y ≥ 100 D) 2X² + 7Y ≥ 50 E) 2X × 7Y ≥ 650

Accepted Answer

The valid constraint is of the form Ax + By ≥ C, where A, B, and C are constants and x and y are decision variables. Option C is the only one in this form, and thus it is the valid constraint. Options A, B, D, and E are either not in the correct form or have incorrect coefficients.

Question 7

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 is true. The product-mix linear programming problem is a type of optimization problem commonly used in business and economics to determine the optimal combination of products or services to produce in order to maximize profit while taking into account constraints such as limited resources or production capacity.

Question 8

The region that satisfies all of the constraints in graphical linear programming is called the region of optimality.

Accepted Answer

The region that satisfies all of the constraints in graphical linear programming is called the feasible region, not the region of optimality. The region of optimality refers to the specific points within the feasible region that optimize (maximize or minimize) the objective function.

Question 9

Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.

Accepted Answer

The correct method is to move the objective function line (not iso-profit line) to each corner of the feasible region until the optimum is identified.

Question 10

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 that is used to optimize decisions among alternative courses of action. It is applicable in situations where there are limited resources that can be allocated to different activities to achieve the desired outcome. Therefore, this statement is false.

Question 11

The region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

Accepted Answer

The origin (0,0) is not included in the region that satisfies the constraint 4X + 15Z ≥ 1000, since any value of X and Z that satisfies this inequality must be greater than zero.

Question 12

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 a mathematical equation for the objective function in a linear programming problem.

Question 13

In sensitivity analysis, a zero shadow price (or dual value) for a resource ordinarily means that the resource has not been used up.

Accepted Answer

A zero shadow price for a resource means that the resource has not been fully utilized and there is still some available capacity.

Question 14

The optimal solution to a linear programming problem is within the feasible region.

Accepted Answer

The feasible region is the set of all possible solutions that satisfy the constraints of the linear programming problem. The optimal solution is the point within this region that maximizes or minimizes the objective function. Therefore, the optimal solution must always lie within the feasible region.

Question 15

In linear programming, statements such as "the blend must consist of at least 10% of ingredient A, at least 30% of ingredient B, and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100%.

Accepted Answer

In linear programming, constraints are not required to add up to 100%, as long as they ensure the feasibility of the solution. In this case, the constraint ensures that the blend contains at least 10% of A, at least 30% of B and no more than 50% of C, which can be achieved even if the percentages do not add up to 100%.

Question 16

In terms of linear programming, the fact that the solution is infeasible implies that the "profit" can increase without limit.

Accepted Answer

Infeasibility implies that there is no feasible solution, i.e. no solution satisfies all constraints. Therefore, it is not possible to increase profit since there is no feasible solution to begin with.

Question 17

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

Accepted Answer

Linear programming is a tool used for optimizing resource allocation and decision making in operations management. It helps in determining the best possible outcome given certain constraints and objectives.

Question 18

Constraints are needed to solve linear programming problems by hand, but not by computer.

Accepted Answer

Constraints are needed for both manual and computerized solving of linear programming problems. Constraints provide limits and boundaries for the variables and determine the feasible region. Without constraints, the problem would not be a linear programming problem but an unconstrained optimization problem.

Question 19

In linear programming, if there are three constraints, each representing a resource that can be used up, the optimal solution must use up all of each of the three resources.

Accepted Answer

The optimal solution may or may not use up all of each of the three resources, depending on the problem's objective function and coefficients. It is possible for there to be slack or surplus variables indicating that not all of the resources are used up at the optimal solution.

Question 20

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 labour 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 successfully applied in all of the mentioned situations. It can help in minimizing cost, maximizing profit, optimizing resources, and making efficient decisions in various industries, including transportation, emergency services, and banking.

Quiz 19: Linear Programming