Question 1

Binding constraints are constraints that hold as an equality.​

Accepted Answer

Binding constraints are constraints that hold as an equality, meaning that they restrict the variables to a specific value. In contrast, non-binding constraints are those that are satisfied as an inequality, meaning that they do not restrict the variables to a specific value but rather set a limit on their possible values.

Question 2

Suppose a firm must at least meet minimum expected demands of 60 for product x and 80 of product y. An algebraic formulation of these constraints is:

Accepted Answer

The answer of Suppose a firm must at least meet...

Question 3

If a manufacturing process takes 3 hours per unit of x and 5 hours per unit of y and a maximum of 100 hours of manufacturing process time are available, then an algebraic formulation of this constraint is:

Accepted Answer

The answer of If a manufacturing process takes 3 hours...

Question 4

In general, the complete solution of a linear programming problem involves three stages: formulating the model, invoking Solver to find the optimal solution, and performing sensitivity analysis.

Accepted Answer

This is the standard three-stage process for solving linear programming problems.

Question 5

The solution of a linear programming problem using Excel^® typically involves the following three stages:

Accepted Answer

The three stages involved in solving a linear programming problem using Excel and Solver are as follows: formulating the problem (which involves identifying the decision variables, objective function, and constraints), invoking Solver (which involves setting up Solver to solve the problem and finding the optimal solution), and sensitivity analysis (which involves changing parameters to analyze the effect on the optimal solution). Graphing the problem may be useful in understanding and visualizing the problem, but it is not a necessary stage in solving the problem using Excel and Solver. Designing decision variable cells, target cells, and constraints is part of formulating the problem, rather than a separate stage. Designing inputs, decision variables, and outputs may be part of the problem formulation, but it is not a three-stage process as described in the question.

Question 6

Nonbinding constraints will always have slack, which is the difference between the two sides of the inequality in the constraint equation.

Accepted Answer

Nonbinding constraints do not affect the optimal solution and therefore will always have slack, which is positive in value.

Question 7

The feasible region in a graphical solution of a linear programming problem will appear as some type of polygon, with lines forming all sides.

Accepted Answer

The feasible region is the region that satisfies all the constraints of the linear programming problem. Since constraints are expressed in the form of linear equations or inequalities, they can be represented graphically as lines or boundaries. The feasible region is the intersection of all these lines, which is typically a polygon with sides formed by the boundaries of the constraints. Therefore, the statement is true.

Question 8

The optimal solution to any linear programming model is the:

Accepted Answer

The optimal solution to a linear programming model is always a corner point of the feasible region, which is a polygon formed by the intersection of the constraints. The objective function is optimized at one or more of these corner points, so the solution is not a maximum or minimum of a parabola or a straight line.

Question 9

Linear programming problems can always be formulated algebraically, but not always on a spreadsheet.

Accepted Answer

Linear programming problems can often be formulated on a spreadsheet using specialized software or add-ons. However, it may not always be easy or practical to do so, especially for large or complex problems, and algebraic formulations may be more appropriate.

Question 10

What is the equation of the line representing this constraint?  ​

Accepted Answer

The answer of What is the equation of the line...

Question 11

The optimal solution to any linear programming model is a corner point of a polygon.

Accepted Answer

This is known as the corner point theorem or the extreme point theorem, which states that the optimal solution to a linear programming problem will always be at one of the corner points or vertices of the feasible region (polygon).

Question 12

A linear programming problem with _____decision variable(s) can be solved by a graphical solution method.

Accepted Answer

A linear programming problem with two decision variables can be easily solved graphically by plotting the constraints and finding the feasible region, and then maximizing or minimizing the objective function by identifying the corner points of the feasible region. The graphical method becomes less practical and more difficult with more decision variables.

Question 13

In determining the optimal solution to a linear programming problem graphically, if the objective is to maximize the objective, we pull the objective function line down until it contacts the feasible region.

Accepted Answer

This is correct. When maximizing, we want to move the objective function line (often represented by a dotted line) upwards until it touches the highest possible point of the feasible region. Similarly, when minimizing, we want to move the objective function line downwards until it touches the lowest possible point of the feasible region.

Question 14

Suppose an objective function has the equation:  .
Then the slope of the objective function line is 2.

Accepted Answer

The equation of an objective function doesn't provide information about the slope of the objective function line. Therefore, we cannot determine the slope of the objective function line from the given equation.

Question 15

There are two primary ways to formulate a linear programming problem: the traditional algebraic way and with spreadsheets.

Accepted Answer

This is true. Linear programming can be formulated using traditional algebraic methods, such as writing out the objective function and constraints as mathematical equations, or it can be formulated using spreadsheets or specialized software.

Question 16

Suppose a constraint has this equation:  Then the slope of the constraint line is -2.

Accepted Answer

The answer of Suppose a constraint has this equation: ...

Question 17

Suppose a company sells two different products, x and y, for net profits of $5 per unit and $10 per unit, respectively. The slope of the line representing the objective function is:

Accepted Answer

The slope of the objective function, which represents the relationship between the profits from products x and y, is calculated as the ratio of the profits per unit of y to x. Thus, the slope = $10/$5 = 2. However, since the slope is typically represented as y over x (rise over run), and in this context, it represents a trade-off or exchange rate between the two products, the correct interpretation should reflect the decrease in x for an increase in y, hence -0.5.

Question 18

Sinclair Plastics operates two chemical plants which produce polyethylene; the Ohio Valley plant, which produces 5000 tons per month, and the Lakeview plant, which can produce 7000 tons per month. Sinclair sells its polyethylene to three different GM auto plants: Grand Rapids (demand = 3000 tons per month), Blue Ridge (demand = 5000 tons per month), and Sunset (demand = 4000 tons per month). The costs of shipping between the respective plants is shown in the table below: 
-What are the decision variables in this problem?

Accepted Answer

The answer of Sinclair Plastics operates two chemical plants which...

Question 19

The prototype linear programming problem is to select an optimal mix of products to produce to maximize profit. This type of problem is referred to as the:

Accepted Answer

The prototype linear programming problem mentioned in the question is commonly known as the product mix problem, where a business has to determine the optimal mix of products that can be produced to maximize its profits. Therefore, option A is the correct answer. Option B (production problem) is a broad term that can refer to various production-related issues, while option C (product/process problem) and option D (product scheduling problem) do not accurately describe the given problem.

Question 20

When formulating a linear programming spreadsheet model, we specify the constraints in a Solver dialog box, since Excel does not show the constraints directly.

Accepted Answer

The answer of When formulating a linear programming spreadsheet model,...

Quiz 13: Introduction to Optimization Modeling