Exam 8: Linear Programming Applications

What is the objective in the truck loading problem?

The following table provides shipping costs from each of two regional warehouses to each of three destinations.The supplies available and the demands are also given in the table. Formulate this as a linear programming problem.Carefully define all decision variables.

Table 8-5 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. T = number of tables produced each week B = number of bookcases produced each week -Referring to Table 8-5,if we were to frame this as a linear programming problem,the objective function would be

Describe the portfolio selection linear programming application.

The following problem type is such a special case of linear programming that a special algorithm has been developed to solve it.

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 -According to Table 8-4,which describes a production problem,what would the objective function be?

Blending problems arise when one must decide which of two or more ingredients is to be chosen to produce a product.

Three types of fertilizer are manufactured by a company: Regular,Supergro,and Jungle Feeder.Regular should have at least 10 percent nitrogen and 16 percent phosphorous.Supergro should have at least 12 percent nitrogen and 20 percent phosphorous,and Jungle Feeder should have at least 15 percent nitrogen and 18 percent phosphorous.These are made by using two components: A and B.Component A costs $0.30 per pound and is 14 percent nitrogen and 18 percent phosphorous.Component B costs $0.50 per pound and is 20 percent nitrogen and 24 percent phosphorous.The demand for Regular is projected to be 1,000 pounds,while each of the others has a demand of 2,000 pounds.Formulate the appropriate linear program.

Describe the production mix linear programming application.

Describe the feed mix linear programming application.

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?

Another name for the transportation problem is the logistics problem.

Friendly Manufacturing has three factories (1,2,and 3)and three warehouses (A,B,and C).The table below shows the shipping costs between each factory (in dollars)and warehouse,the factory manufacturing capabilities (in 1000s),and the warehouse capacities (in 1000s).Write the objective function and the constraint inequalities.Let X_1A = 1000s of units shipped from factory 1 to warehouse A,etc.

The constraints in a transportation problem deal with requirements at each origin and capacities at each destination.

Table 8-2 Diamond Jeweler's is trying to determine how to advertise in order to maximize their exposure.Their weekly advertising budget is $10,000.They are considering three possible media: tv,newspaper,and radio.Information regarding cost and exposure is given in the table below: Let T = the # of tv ads,N = the # of newspaper ads,and R = the # of radio ads -According to Table 8-2,which describes a media selection problem,what would the objective function be?

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

The linear programming truck loading model always results in a practical solution.

Media selection problems are typically approached with LP by either

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.Find the optimal solution and minimum cost.

Production scheduling is amenable to solution by LP because it is a problem that must be solved on a regular basis.