Question 1

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

Accepted Answer

The correct form is: beginning inventory + production - sales = ending inventory. This equation accounts for how much was initially available, adds what was produced, and subtracts what was sold to determine the ending inventory.

Question 2

Portfolio selection problems should acknowledge both risk and return.

Accepted Answer

Portfolio selection involves choosing a combination of assets that maximize the expected return while minimizing the risk. Therefore, both risk and return should be considered in portfolio selection problems.

Question 3

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

When setting up a constraint, the units on both sides of the equation must be the same. Mixing units of measurement can lead to errors in the calculation and incorrect results. Therefore, using minutes on one side and hours on the other side is not acceptable.

Question 4

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 may not take into account certain real-world constraints or factors, and the optimal solution may not always be practical or feasible. A decision maker should carefully consider the LP model output and make adjustments or modifications as necessary to ensure the solution is appropriate for the specific situation.

Question 5

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

Question 6

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 related to the overall cost of production.

Question 7

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 equation correctly expresses the available daily steel and the amount of steel required for each product, using decision variables x₁ and x₂. It also incorporates the fact that the company can produce both products simultaneously.

Question 8

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 company's objective seems to be maximizing profit, but the formula provided is incorrect for calculating profit. The correct approach would involve calculating the profit per unit for each product (selling price - variable cost) and then maximizing the total profit, not simply adding the selling prices and subtracting a combined cost figure.

Question 9

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

Accepted Answer

In some cases, a problem may have multiple optimal solutions due to the complexity and multiple factors involved in real-world scenarios. These multiple solutions can arise based on different criteria or constraints that are set for the problem. Therefore, the statement is false.

Question 10

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

Accepted Answer

Double-subscript notation is often used in mathematical modeling to represent variables that are associated with two different dimensions, such as rows and columns in a matrix, or time and location in scheduling problems. It is not about the number of decision variables but about the structure and relationships between them.

Question 11

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 stated that at least 40% of the interviews must be in the evening. This means that the proportion of evening interviews must be greater than or equal to 0.4. We can represent this constraint as 0.4 <= E / (D + E), which simplifies to E >= 0.4D + 0.4E or -0.4D + 0.6E > 0.

Question 12

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 a common assumption in multiperiod production scheduling problems, as it simplifies the modeling and is consistent with the idea that any remaining inventory at the end of a period will be carried over to the next period as starting inventory.

Question 13

Revenue management methodology was originally developed for the banking industry.

Accepted Answer

Revenue management methodology was actually developed in the airline industry in the 1980s, not the banking industry. It has since been applied to other industries such as hospitality, entertainment, and transportation.

Question 14

​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 15

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 not the nonnegativity constraint on decision variables, but rather that it requires the relationships between the variables to be linear. This means all equations in the model (objective function and constraints) must be linear equations.

Question 16

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

This statement is true as media selection can be approached from different perspectives - either to maximize exposure quality or to maximize the number of customers reached. In both cases, constraints such as budget, target audience, and message consistency need to be taken into consideration.

Question 17

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

Accepted Answer

Dual prices represent the marginal value of resources or constraints in the objective function. Therefore, understanding how costs were allocated to the constraints is essential in interpreting the dual prices correctly.

Question 18

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

Accepted Answer

Real-world problems are often more complex than textbook problems and involve many variables and constraints that need to be considered in order to find a solution. These variables may include factors such as time, cost, resource availability, and environmental impact, making the problem much more challenging to solve than a simple mathematical equation.

Question 19

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

Accepted Answer

If an LP problem is not correctly formulated, the computer software may not be able to solve it at all or may produce incorrect results, but it will not necessarily indicate it is infeasible. The infeasibility message only occurs when the constraints of the problem conflict with each other or with the objective function.

Question 20

​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 LP models can involve collecting and processing vast amounts of data from various sources, which can be a time-consuming process. Formulating and solving the LP model may be relatively quicker once the data is available.

Quiz 9: LP Applications

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