Question 1

A mutual fund manager must decide how much money to invest in Atlantic Oil (A)and how much to invest in Pacific Oil (P).At least 60% of the money invested in the two oil companies must be in Pacific Oil.A correct modeling of this constraint is
A)0.4A + 0.6P > 0.
B)-0.4A + 0.6P > 0.
C)0.6A + 0.4P > 0.
D)-0.6A + 0.4P > 0.

Accepted Answer

The constraint states that the investment in Pacific Oil should be at least 60% of the total investment. This can be written as 0.6(A+P) <= P. Simplifying, we get 0.4A >= -0.4P, which can be rearranged as -0.6A + 0.4P > 0. Therefore, the correct modeling of the constraint is option D.

Question 2

Blending problems arise whenever a manager must decide how to
A)mix several different asset types in one investment strategy.
B)mix two or more resources to produce one or more products.
C)combine the results of two or more research studies into one.
D)allocate workers with different skill levels to various work shifts.

Accepted Answer

Blending problems involve the mixing of two or more resources to produce one or more products. This is the only option that accurately describes a blending problem.

Question 3

An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time,radio time,and newspaper ads.Information about each medium is shown below.  If the number of TV ads cannot exceed the number of radio ads by more than 4,and if the advertising budget is $10,000,develop the model that will maximize the number reached and achieve an exposure quality of at least 1000.​
​

Accepted Answer

The answer of An ad campaign for a new snack...

Question 4

Tots Toys Company is trying to schedule production of two very popular toys for the next three months: a rocking horse and a scooter.Information about both toys is given below.  ​  ​
Develop a model that would tell the company how many of each toy to produce during each month.You are to minimize total cost.Inventory cost will be levied on any items in inventory on June 30,July 31,or August 31 after demand for the month has been satisfied.Your model should make use of the relationship:
Beginning inventory + Production − Demand = Ending inventory
for each month.The company wants to end the summer with 150 rocking horses and 60 scooters as beginning inventory for September 1.Don't forget to define your decision variables.

Accepted Answer

The answer of Tots Toys Company is trying to schedule...

Question 5

An LP model for 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.There is a constraint that HD ≥ 100.The solution indicates that interviewing another homeowner during the day will increase costs by 10.00.What does this tell you about the HD variable? ​
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

The answer of An LP model for a marketing research...

Question 6

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 correct equation for calculating the net hours in department 3 after transfers is to start with the initial hours allocated to department 3 (A₃), subtract hours transferred out to departments 1 and 2 (T₁₃ and T₂₃), and add hours transferred in from departments 2 and 4 (T₃₂ and T₃₄). This results in the net hours being equal to 2500.

Question 7

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 ≤ 5.
B)A − 0.5B + C ≤ 0.
C)0.5A − B − 0.5C ≤ 0.
D)−0.5A + 0.5B − 0.5C ≤ 0.

Accepted Answer

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

Question 8

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

Media selection problems typically focus on determining the optimal number of times to use each media source to achieve advertising goals within budget constraints.

Question 9

Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly,a seat and frame unit,and rear wheels.The company has orders for 12,000 of these tricycles.Current schedules yield the following information:  The company obviously does not have the resources available to manufacture everything needed for the completion of 12,000 tricycles so it has gathered purchase information for each component.Develop a linear programming model to tell the company how many of each component should be manufactured and how many should be purchased in order to provide 12,000 fully completed tricycles at the minimum cost.

Accepted Answer

The answer of Tots Toys makes a plastic tricycle that...

Question 10

Information on a prospective investment for Wells Financial Services is given below.  ​
In each period,funds available for investment come from two sources: loan funds and income from the previous period's investment.Expenses,or cash outflows,in each period must include repayment of the previous period's loan plus 8.5% interest,and the current payroll payment.In addition,to end the planning horizon,investment income from period 4 (at 110% of the investment)must be sufficient to cover the loan plus interest from period 4.The difference in these two quantities represents net income and is to be maximized.How much should be borrowed,and how much should be invested each period?
​

Accepted Answer

The answer of Information on a prospective investment for Wells...

Question 11

Which operations management application model is most likely to have an objective function that minimizes the sum of manufacturing costs,purchasing costs,and overtime costs?
A)blending
B)make-or-buy decision
C)workforce assignment
D)production scheduling

Accepted Answer

The make-or-buy decision model focuses on determining whether it is more cost-effective to produce goods in-house or purchase them from an external supplier. This model inherently considers manufacturing costs (if made in-house), purchasing costs (if bought), and potentially overtime costs if the decision impacts the need for additional labor hours to meet production demands.

Question 12

Blending problems occur frequently in which of the following industries?
A)chemical
B)petroleum
C)food services
D)All of these are correct.

Accepted Answer

Blending problems occur frequently in all of these industries as they involve the mixing of various components in precise proportions to achieve the desired end product. In the chemical industry, blending is important for the production of pharmaceuticals, paints, cosmetic products, etc. In the petroleum industry, blending is necessary to produce fuels with desired properties such as octane rating and viscosity. In the food services industry, blending is critical to ensure consistency and taste in food products.

Question 13

The dual price for a constraint that compares funds used with funds available is 0.058.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 dual price indicates the value of relaxing the constraint by one unit. If additional funds can be obtained at a rate lower than the dual price (5.8%), it is beneficial to acquire them, as they would contribute positively to the objective function.

Question 14

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,we would express it as A)P₂₁ + P₂₂ + P₂₃ ≤ 400. B)P₁₂ + P₂₂ + P₃₂ ≤ 400. C)P₃₂ ≤ 400. D)P₂₃ ≤ 400.

Accepted Answer

The given formula P_ij represents the production of product i in period j. To express the limit on production of the company's three products in period 2 as 400, we need to add the production of all three products in period 2 and set it less than or equal to 400. Option B has the correct combination of products and time periods to satisfy this condition, as it includes the production of all three products in period 2 (P₁₂ + P₂₂ + P₃₂) and sets it less than or equal to 400. Option A includes the wrong time period for one of the products, while options C and D only consider one product at a time.

Question 15

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,we would write it as A)P₁₃ − P₁₄ ≤ 100; P₁₄ − P₁₃ ≤ 100. B)P₁₃ − P₁₄ ≤ 100; P₁₃ − P₁₄ ≥ 100. C)P₁₃ − P₁₄ ≤ 100; P₁₄ − P₁₃ ≥ 100. D)P₁₃ − P₁₄ ≥ 100; P₁₄ − P₁₃ ≥ 100.

Accepted Answer

To specify that production of product 1 in period 3 and period 4 differs by no more than 100 units, we need to write two inequalities, one for each possible direction of the difference. The first inequality would be P₁₃ - P₁₄ ≤ 100, indicating that the production in period 3 cannot be more than 100 units greater than the production in period 4. The second inequality would be P₁₄ - P₁₃ ≤ 100, indicating that the production in period 4 cannot be more than 100 units greater than the production in period 3. Therefore, the correct choice is A, which includes both of these inequalities.

Question 16

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 process of gathering and analyzing information about consumer characteristics, attitudes, and preferences in order to make informed business decisions. Client satisfaction processing, capital budgeting, and production planning are not directly related to the study of consumer behavior.

Question 17

The production scheduling problem modeled in the textbook involves capacity constraints on all of the following types of resources EXCEPT
A)material.
B)labor.
C)machine.
D)storage.

Accepted Answer

Material is not typically considered a capacity constraint in production scheduling problems. Capacity constraints usually involve resources that limit the production rate or volume, such as labor, machines, and storage, but not the materials being used in production.

Question 18

A&C Distributors represents many outdoor products companies and schedules deliveries to discount stores,garden centers,and hardware stores.Currently,scheduling needs to be done for two lawn sprinklers,the Water Wave and Spring Shower models.Requirements for shipment to a warehouse for a national chain of garden centers are shown below. Let S_ij be the number of units of sprinkler i shipped in month j,where i = 1 or 2,and j = 1,2,or 3.Let W_ij be the number of sprinklers that are at the warehouse at the end of a month,in excess of the minimum requirement.

Accepted Answer

The answer of A&C Distributors represents many outdoor products companies...

Question 19

Let M be the number of units to make and let 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 + 12,000B.
D)Min 2M + 3B.

Accepted Answer

The objective function represents the total cost to satisfy the need for 4000 units, where making a unit costs $2 and buying a unit costs $3. The goal is to minimize this cost, hence "Min 2M + 3B" correctly represents the objective of minimizing the total cost of making and buying the units.

Question 20

In a production scheduling LP,the demand requirement constraint for a time period takes the form
A)Beginning inventory + Production + Ending inventory > Demand.
B)Beginning inventory -Production - Ending inventory = Demand.
C)Beginning inventory + Production - Ending inventory = Demand.
D)Beginning inventory - Production - Ending inventory > Demand.

Accepted Answer

The demand requirement constraint should ensure that the beginning inventory plus the production during the time period minus the ending inventory should be equal to or greater than the demand for that time period. Option C accurately represents this relationship. Option A and D have an inequality sign instead of an equation sign, and option B has a plus sign instead of a minus sign.

Quiz 4: Linear Programming Applications in Marketing, finance, and OM

A mutual fund manager must decide how much money to invest in Atlantic Oil (A) and how much to invest in Pacific Oil (P) .At least 60% of the money invested in the two oil companies must be in Pacific Oil.A correct modeling of this constraint is

Blending problems arise whenever a manager must decide how to

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

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

Which operations management application model is most likely to have an objective function that minimizes the sum of manufacturing costs,purchasing costs,and overtime costs?

Blending problems occur frequently in which of the following industries?

The dual price for a constraint that compares funds used with funds available is 0.058.This means that

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,we would express it as

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,we would write it as

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

The production scheduling problem modeled in the textbook involves capacity constraints on all of the following types of resources EXCEPT

Let M be the number of units to make and let 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

In a production scheduling LP,the demand requirement constraint for a time period takes the form