Question 1

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

Accepted Answer

While correct problem formulation reduces the likelihood of having multiple optimal solutions, it is still possible for complex problems and decision-making situations to have multiple equally good solutions.

Question 2

Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then
A)B $\le$ 5
B)A - .5B + C $\le$ 0
C).5A - B - .5C $\le$0
D)-.5A + .5B - .5C $\le$ 0

Accepted Answer

The condition "no more than 50% of the total investment can be in company B" translates to B $\le$ 0.5(A + B + C). Simplifying this inequality gives -.5A + .5B - .5C $\le$ 0.

Question 3

A marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories and there is a constraint that HD $\ge$ 100. The solution indicates that interviewing another homeowner during the day will increase costs by 10.00. What do you know?
A)the objective function coefficient of HD is 10.
B)the dual price for the HD constraint is 10.
C)the objective function coefficient of HD is -10.
D)the dual price for the HD constraint is -10.

Accepted Answer

D

Question 4

Media selection problems usually determine
A)how many times to use each media source.
B)the coverage provided by each media source.
C)the cost of each advertising exposure.
D)the relative value of each medium.

Accepted Answer

The answer of Media selection problems usually determine
A)how many times...

Question 5

The objective function for portfolio selection problems usually is maximization of expected return or
A)maximization of investment types
B)minimization of cost
C)minimization of risk
D)maximization of number of shares

Accepted Answer

The objective function for portfolio selection is to minimize risk or maximize return. Since the question specifically asks about the objective function, the best choice is C which minimizes risk. A and D are incorrect as they do not relate to the objective function, and B is incorrect as it is not typically the objective function in portfolio selection problems.

Question 6

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

Accepted Answer

If the LP problem is not correctly formulated, the computer software may not be able to solve it or may provide erroneous results. It may not necessarily indicate that the problem is infeasible.

Question 7

For a portfolio selection problem with the objective of maximizing expected return, the dual price for the available funds constraint provides information about the
A)proportion of the portfolio that is invested in a particular investment type
B)return from additional investment funds
C)degree of portfolio diversification that is optimal
D)cost of an additional unit of a particular investment type

Accepted Answer

The dual price for the available funds constraint indicates the increase in the objective function (expected return) for each additional unit of funds available, reflecting the return from additional investment funds.

Question 8

Department 3 has 2500 hours. Transfers are allowed to departments 2 and 4, and from departments 1 and 2. If A_i measures the labor hours allocated to department i and T_ij the hours transferred from department i to department j, then A)T₁₃ + T₂₃ - T₃₂ -T₃₄ - A₃ = 2500 B)T₃₁ + T₃₂ - T₂₃ -T₄₃ + A₃ = 2500 C)A₃ + T₁₃ + T₂₃ -T₃₂ - T₃₄ = 2500 D)A₃ - T₁₃ - T₂₃ + T₃₂ + T₃₄ = 2500

Accepted Answer

The answer of Department 3 has 2500 hours. Transfers are...

Question 9

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

Accepted Answer

Dual prices represent the rate of change in the optimal objective function value with respect to a small change in the right-hand-side value of a constraint, assuming all other constraints and the objective function coefficients remain the same. Therefore, to properly interpret dual prices, one must understand how the costs were allocated in the objective function.

Question 10

If P_ij = the production of product i in period j, then to indicate that the limit on production of the company's three products in period 2 is 400, A)P₂₁ + P₂₂ + P₂₃ $\le$400 B)P₁₂ + P₂₂ + P₃₂ $\le$ 400 C)P₃₂ $\le$ 400 D)P₂₃ $\le$ 400

Accepted Answer

The given formula P_ij denotes the production of product i in period j. To indicate the limit on production of the company's three products in period 2, we need to add the production of all three products in that period and set it less than or equal to 400. In option B, P₁₂ + P₂₂ + P₃₂ F1F1F1S1 is the sum of the production of all three products in period 2, and it is set to be less than or equal to 400. Thus, option B is the best choice.

Question 11

Let P_ij = the production of product i in period j. To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units, A)P₁₃ -P₁₄ $\le$ 100; P₁₄ -P₁₃ $\le$100 B)P₁₃ - P₁₄ $\le$100; P₁₃ -P₁₄ $\ge$ 100 C)P₁₃ -P₁₄ $\le$ 100; P₁₄ -P₁₃ $\ge$ 100 D)P₁₃ - P₁₄ $\ge$ 100; P₁₄ - P₁₃ $\ge$ 100

Accepted Answer

To ensure the production difference is no more than 100 units, both P₁₃ - P₁₄ ≤ 100 and P₁₄ - P₁₃ ≤ 100 must hold.

Question 12

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 13

The dual price for a constraint that compares funds used with funds available is .058. This means that
A)the cost of additional funds is 5.8%.
B)if more funds can be obtained at a rate of 5.5%, some should be.
C)no more funds are needed.
D)the objective was to minimize.

Accepted Answer

The answer of The dual price for a constraint that...

Question 14

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 from either perspective, depending on the specific goals and constraints of the marketing campaign.

Question 15

For the marketing research problem presented in the textbook, the research firm's objective is to conduct the market survey so as to meet the client's needs at a minimum cost.

Accepted Answer

The textbook states that the research firm's objective is "to conduct a market survey at a minimum cost so as to meet the client's needs."

Question 16

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

Accepted Answer

The answer of Production constraints frequently take the form:
beginning inventory...

Question 17

Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is
A)Max 2M + 3B
B)Min 4000 (M + B)
C)Max 8000M + 12000B
D)Min 2M + 3B

Accepted Answer

The answer of Let M be the number of units...

Question 18

To study consumer characteristics, attitudes, and preferences, a company would engage in
A)client satisfaction processing.
B)marketing research.
C)capital budgeting.
D)production planning.

Accepted Answer

Marketing research is the systematic gathering, recording, and analyzing of data related to marketing a particular product or service. It helps a company to understand consumer characteristics, attitudes, and preferences, which in turn helps to design effective marketing strategies. Client satisfaction processing, capital budgeting, and production planning are not directly related to studying consumer characteristics, attitudes, and preferences.

Question 19

Portfolio selection problems should acknowledge both risk and return.

Accepted Answer

Portfolio selection involves choosing investments that offer a balance of both risk and return. Ignoring either factor can lead to suboptimal investment decisions.

Question 20

An LP model for a large-scale production scheduling problem involving numerous products, machines, and time periods can require thousands of decision variables and constraints.

Accepted Answer

LP models for large-scale production scheduling problems can involve thousands of decision variables and constraints due to the complexity of the problem involving many products, machines, and time periods.

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

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

Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, then

Media selection problems usually determine

The objective function for portfolio selection problems usually is maximization of expected return or

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

For a portfolio selection problem with the objective of maximizing expected return, the dual price for the available funds constraint provides information about the

Department 3 has 2500 hours. Transfers are allowed to departments 2 and 4, and from departments 1 and 2. If Ai measures the labor hours allocated to department i and Tij the hours transferred from department i to department j, then

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

If Pij = the production of product i in period j, then to indicate that the limit on production of the company's three products in period 2 is 400,

Let Pij = the production of product i in period j. To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units,

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

The dual price for a constraint that compares funds used with funds available is .058. This means that

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.

For the marketing research problem presented in the textbook, the research firm's objective is to conduct the market survey so as to meet the client's needs at a minimum cost.

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

Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is

To study consumer characteristics, attitudes, and preferences, a company would engage in

Portfolio selection problems should acknowledge both risk and return.

An LP model for a large-scale production scheduling problem involving numerous products, machines, and time periods can require thousands of decision variables and constraints.

Department 3 has 2500 hours. Transfers are allowed to departments 2 and 4, and from departments 1 and 2. If A_i measures the labor hours allocated to department i and T_ij the hours transferred from department i to department j, then

If P_ij = the production of product i in period j, then to indicate that the limit on production of the company's three products in period 2 is 400,

Let P_ij = the production of product i in period j. To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units,