Exam 8: Linear Programming Applications

Table 8-3 Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood. -Referring to Table 8-3, which of the following constraints would be used?

Linear programming variable names such as X₁₁, X₁₂, X₁₃, could possibly be used to represent production of a product (X_1j ) over several months.

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).

The linear programming ingredient or blending problem model allows one to include not only the cost of the resource, but also the differences in composition.

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: -According to Table 8-1, which describes a production problem, what would the objective function be?

Describe the feed mix linear programming application.

Media selection problems are typically approached with LP by either

Transporting goods from several origins to several destinations efficiently is called the transportation problem.

What is the objective in the diet problem?

Table 8-4 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 Exhibit 8-4, which describes a labor planning problem and its solution, how many workers would be assigned to shift 4?

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

The linear programming model of the production mix problem only includes constraints of the less than or equal form.

Describe the production mix linear programming application.

Table 8-4 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 8-4, which describes a labor planning problem and its solution, how many workers would actually be on duty during shift 1?

Table 8-4 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 8-4, which describes a labor planning problem and its solution, how many workers would be assigned to shift 3?

A marketing research linear programming model can help a researcher structure the least expensive, statistically meaningful sample.

Table 8-3 Each coffee table produced by Timothy Kent Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Kent's firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood. -Referring to Table 8-3, the solution to the problem is

The linear programming transportation model allows us to solve problems where supply does not equal demand.

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

Describe the shipping problem linear programming application.