Question 1

If a real-world problem is correctly formulated, it is not possible to have alternative optimal solutions.

Accepted Answer

Alternative optimal solutions can exist if multiple solutions yield the same optimal value for the objective function in a correctly formulated problem.

Question 2

Double-subscript notation for decision variables should be avoided unless the number of decision variables exceeds nine.

Accepted Answer

Double-subscript notation can be used for any number of decision variables, but it should be used with caution as it can become difficult to read and interpret, especially for larger problem instances.

Question 3

The primary limitation of linear programming's applicability is the requirement that all decision variables be nonnegative.

Accepted Answer

The primary limitation of linear programming is its requirement for linearity in the equations that model the relationships among variables, not the nonnegativity constraint on decision variables.

Question 4

Revenue management methodology was originally developed for the banking industry.

Accepted Answer

Revenue management methodology was originally developed for the airline industry. It was later adopted by other industries such as hotels, car rental agencies, and restaurants.

Question 5

A company makes two products from steel; one requires 2 tons of steel and the other requires 3 tons. There are 100 tons of steel available daily. A constraint on daily production could be written as: 2x₁ + 3x₂ ≤ 100.

Accepted Answer

The constraint represents the total steel used by both products, ensuring it does not exceed the available 100 tons.

Question 6

To properly interpret dual prices, one must know how costs were allocated in the objective function.

Accepted Answer

Dual prices are only meaningful if one knows how costs were allocated in the objective function. Dual prices represent the amount by which the objective function value increases if an additional unit of a resource or constraint is relaxed or increased. However, the amount of increase depends on how the costs were allocated in the objective function. Therefore, understanding the allocation of costs is necessary for proper interpretation of dual prices.

Question 7

A marketing research firm must determine how many daytime interviews (D) and evening interviews (E) to conduct. At least 40% of the interviews must be in the evening. A correct modeling of this constraint is: -0.4D + 0.6E > 0.​

Accepted Answer

The constraint states that at least 40% of the interviews must be in the evening. This can be mathematically represented as 0.4(D+E) <= E or 0.6D >= 0.4E, which can be further simplified as -0.4D + 0.6E > 0. Therefore, the correct modeling of this constraint is -0.4D + 0.6E > 0, making option A the correct answer.

Question 8

For the multiperiod production scheduling problem in the textbook, period n − 1's ending inventory variable was also used as period n's beginning inventory variable.

Accepted Answer

This is true. The ending inventory of one period becomes the beginning inventory of the next period in a multiperiod production scheduling problem.

Question 9

Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time.

Accepted Answer

Converting units is important in ensuring that the constraint is accurate and consistent. Mixing units of measurement on both sides of a constraint can lead to errors and inconsistencies in calculations. Therefore, it is important to use the same unit of measurement on both sides of a constraint.

Question 10

Portfolio selection problems should acknowledge both risk and return.

Accepted Answer

Portfolio selection problems involve choosing a combination of assets that balance the trade-off between risk and return. Both factors need to be considered to create an optimal portfolio that meets the investor's objectives. Ignoring either one could lead to suboptimal outcomes. Therefore, portfolio selection problems need to acknowledge both risk and return.

Question 11

​Data collection for large-scale LP models can be more time-consuming than either the formulation of the model or the development of the computer solution.

Accepted Answer

Data collection for large-scale linear programming (LP) models often involves gathering and processing large amounts of information, which can be more time-consuming than the mathematical formulation or coding of the model.

Question 12

A company makes two products, A and B. A sells for $100 and B sells for $90. The variable production costs are $30 per unit for A and $25 for B. The company's objective could be written as: MAX 190x₁ − 55x₂.

Accepted Answer

The objective function should maximize profit, which is revenue minus costs. The correct expression would be MAX (100x₁ - 30x₁) + (90x₂ - 25x₂), simplifying to MAX 70x₁ + 65x₂.

Question 13

If an LP problem is not correctly formulated, the computer software will indicate it is infeasible when trying to solve it.

Accepted Answer

A poorly formulated LP problem may result in errors, incorrect solutions, or unbounded solutions, but not necessarily an infeasibility indication.

Question 14

Compared to the problems in the textbook, real-world problems generally require more variables and constraints.

Accepted Answer

Real-world problems often involve more complex systems and factors, which require more variables and constraints to accurately model and solve. Textbook problems are usually simplified and only involve a few variables and constraints for the sake of learning and practicing problem-solving techniques.

Question 15

Production constraints frequently take the form:
beginning inventory + sales − production = ending inventory

Accepted Answer

The correct form of the production constraint is: beginning inventory + production - sales = ending inventory. This equation ensures that the inventory is adjusted correctly based on production and sales.

Question 16

​The marketing research model presented in the textbook involves minimizing total interview cost subject to interview quota guidelines.

Accepted Answer

The marketing research model presented in the textbook does involve minimizing total interview cost subject to interview quota guidelines.

Question 17

It is improper to combine manufacturing costs and overtime costs in the same objective function.

Accepted Answer

Manufacturing costs and overtime costs can both be components of the total cost objective in operations research or cost optimization problems, as they are both relevant to the overall cost of production.

Question 18

Media selection problems can maximize exposure quality and use number of customers reached as a constraint, or maximize the number of customers reached and use exposure quality as a constraint.

Accepted Answer

Media selection problems can be approached with different objectives, such as maximizing exposure quality or maximizing the number of customers reached. These objectives can be used as constraints, depending on the specific goals of the campaign.

Question 19

A decision maker would be wise to not deviate from the optimal solution found by an LP model because it is the best solution.

Accepted Answer

LP models are mathematical models that use linear programming to find the optimal solution to a given problem. However, LP models are based on certain assumptions, and these assumptions may not always hold in the real world. Additionally, LP models are only as good as the data that is inputted into them. Therefore, while the optimal solution found by an LP model may be a good starting point, it is important for decision makers to take into account other factors such as intuition, experience, and judgment when making decisions.

Question 20

The media selection model presented in the textbook involves maximizing the number of potential customers reached subject to a minimum total exposure quality rating.

Accepted Answer

The media selection model typically involves maximizing exposure or reach while considering constraints like budget, not necessarily a minimum total exposure quality rating.

Quiz 4: Linear Programming Applications in Marketing, Finance, and Operations Management