Exam 8: Linear Programming Applications

A cruise line is planning its menu for the next trip.Vacationers like eating steak,lobster,and chicken.The cruise line has decided to plan for at least half of all booked passengers to have a steak dinner,for at least a quarter of all passengers to have lobster,and the rest to have chicken.Steak dinners cost the company $8,lobsters cost $15,and chicken costs the line $4.On the next cruise,there are 400 passengers booked.In addition,the cruise line has decided to plan for an additional 25% more meals than bookings.Formulate the appropriate linear program.

Media selection problems can be approached with LP from which two perspectives?

Table 8-1 A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows: T = number of tables produced each week C = number of chairs produced each week -According to Table 8-1,which describes a production problem,suppose it is decided that the number of hours used in the assembly process must be at least 90 percent of the number of hours used in the finishing department.How would this constraint be written?

An ingredient or blending problem is a special case of the more general problem known as diet and feed mix problems.

In formulating the media selection linear programming model,we are unable to take into account the effectiveness of a particular presentation (e.g. ,the fact that only 5 percent of the people exposed to a radio ad will respond as desired).

Table 8-1 A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows: T = number of tables produced each week C = number of chairs produced each week -According to Table 8-1,which describes a production problem,which of the following would be a necessary constraint in the problem?

Linear programming is usually used by managers involved in portfolio selection to

Which of the following is considered a decision variable in the media selection problem of maximizing audience exposure?

The linear programming approach to media selection problems is typically to either maximize the number of ads placed per week or to minimize advertising costs.

Which of the following statements is true regarding the labor planning problem?

Table 8-6 The following is a linear programming formulation of a labor planning problem.There are four overlapping shifts,and management must decide how many employees to schedule to start work on each shift.The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day.The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4). -According to Table 8-6,which describes a labor planning problem and its solution,how many workers would be assigned to shift 3?

Table 8-6 The following is a linear programming formulation of a labor planning problem.There are four overlapping shifts,and management must decide how many employees to schedule to start work on each shift.The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day.The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4). -According to Table 8-6,which describes a labor planning problem and its solution,how many workers would be assigned to shift 2?

A media selection LP application describes a method in which media producers select customers.

The selection of specific investments from among a wide variety of alternatives is the type of LP problem known as

Table 8-1 A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 3 hours of assembly,2 hours of finishing,and 1 hour of inspection.Each chair requires 2 hours of assembly,2 hours of finishing,and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently,each week there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows: T = number of tables produced each week C = number of chairs produced each week -According to Table 8-1,which describes a production problem,what would the objective function be?

Table 8-4 A small furniture manufacturer produces tables and chairs.Each product must go through three stages of the manufacturing process: assembly,finishing,and inspection.Each table requires 4 hours of assembly,3 hours of finishing,and 1 hour of inspection.Each chair requires 3 hours of assembly,2 hours of finishing,and 2 hours of inspection.The selling price per table is $140 while the selling price per chair is $90.Currently,each week there are 220 hours of assembly time available,160 hours of finishing time,and 45 hours of inspection time.Assume that one hour of assembly time costs $5.00;one hour of finishing time costs $6.00;one hour of inspection time costs $4.50;and that whatever labor hours are not required for the table and chairs can be applied to another product.Linear programming is to be used to develop a production schedule.Define the variables as follows: T = number of tables produced each week C = number of chairs produced each week -Suppose that the problem described in Table 8-4 is modified to specify that one-third of the tables produced must have 6 chairs,one-third must have 4 chairs,and one-third must have 2 chairs.How would this constraint be written?

A computer start-up named Pear is considering entering the U.S.market with what they believe to be a smaller and faster computer than some of the existing products on the market.They want to get a feel for whether or not customers would be willing to switch from some of the existing bigger brands to consider their product.They want to collect a reasonable sample from across the U.S.representative of all age brackets.They have split the United States into 2 regions: East and West.They want at least 65% of their sample to cover the East and no fewer than 25% of the West.They also have divided the age groups into 3 categories: 18-35,36-69,and 70 and up.They want at least 50% of their sample to be between 18-35 and at least 40% to be between 36-69.The costs per person surveyed is given in the table below: Assume that at least 1,000 people are to be surveyed.The problem is for Pear Company to decide how many people to survey from each age bracket within each region in order to minimize costs while meeting requirements.Formulate this problem as a linear program.

What are the decision variables in the diet problem?

Table 8-6 The following is a linear programming formulation of a labor planning problem.There are four overlapping shifts,and management must decide how many employees to schedule to start work on each shift.The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day.The variables X₁ - X₄ represent the number of employees starting work on each shift (shift 1 through shift 4). -According to Table 8-6,which describes a labor planning problem and its solution,how many workers would be assigned to shift 4?

Describe the marketing research linear programming application.