Exam 8: Linear Programming Applications

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.

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.To keep a balance,the number of chairs produced should be at least twice the number of tables.Also,the number of chairs cannot exceed six times the number of tables.How many tables and chairs should the furniture manufacturer produce to maximize profit?

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

Table 8-3 A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education.There are different cost implications for the region of the country where the college is located and the type of degree.The survey cost table is provided below: The requirements for the survey are as follows: 1.The survey must have at least 1500 students 2.At least 400 graduate students 3.At least 100 graduate students should be from the West 4.No more than 500 undergraduate students should be from the East 5.At least 75 graduate students should be from the Central region 6.At least 300 students should be from the West The marketing research firm would like to minimize the cost of the survey while meeting the requirements.Let X₁ = # of undergraduate students from the East region,X₂ = # of graduate students from the East region,X₃ = # of undergraduate students from the Central region,X₄ = # of graduate students from the Central region,X₅ = # of undergraduate students from the West region,and X₆ = # of graduate students from the West region. -According to Table 8-3,what is the objective function?

If a linear programming problem has alternate solutions,the order in which you enter the constraints may affect the particular solution found.

Since the production mix linear program applications are a special situation,the number of decision variables is limited to two.

The linear programming model of the production scheduling process is usually used when we have to schedule the production of multiple products,each of which requires a set of resources not required by the other products,over time.

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

Using linear programming to maximize audience exposure in an advertising campaign is an example of the type of linear programming application known as

Table 8-7 Ivana Myrocle wishes to invest her inheritance of $200,000 so that her return on investment is maximized,but she also wishes to keep her risk level relatively low.She has decided to invest her money in any of three possible ways: CDs,which pay a guaranteed 6 percent;stocks,which have an expected return of 13 percent;and a money market mutual fund,which is expected to return 8 percent.She has decided that any or all of the $200,000 may be invested,but any part (or all)of it may be put in any of the 3 alternatives.Thus,she may have some money invested in all three alternatives.In formulating this as a linear programming problem,define the variables as follows: C = dollars invested in CDs S = dollars invested in stocks M = dollars invested in the money market mutual fund -According to Table 8-7,which describes an investment problem,which of the following would be the most appropriate constraint in the linear programming problem?

What is another name for blending problems?

The shipping problem in LP is also called the

Three types of gasoline are manufactured by a company - Regular,Super,and Extra.Regular should have at least 11 percent additive 1 and 17 percent additive 2.Super should have at least 13 percent additive 1 and 22 percent additive 2.Extra should have at least 17 percent additive 1 and 19 percent additive 2.These are made by using two crudes - A and B.Crude A cost $28 per barrel and is 14 percent additive 1 and 18 percent additive 2.Crude B costs $30 per barrel and is 20 percent additive 1 and 24 percent additive 2.The demand for Regular is projected to be 1,000 barrels,while each of the others has a demand of 2,000 barrels.Formulate this as a linear programming problem to minimize cost while meeting all constraints.Carefully define all decision variables.

Which of the following is considered a decision variable in the production mix problem of maximizing profit?

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,which of the following constraints would be used?

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 there must be 4 chairs produced for every table.How would this constraint be written?

Green Grass,Inc.just ran out of stock and suddenly has two emergency orders for grass seed blends: one is for 1500 pounds of normal,the other for 2300 pounds of special.At least each pound of normal should contain 60 percent annual seed,while each pound of special should contain at least 70 percent perennial seed.Green Grass has two input mixtures,A and B.Mixture A contains 80 percent perennial and 15 percent annual seed.Mixture B contains 70 percent annual and 25 percent perennial seed.Mixture A costs 90 cents per pound and mixture B costs 50 cents per pound.Set up the constraints and the objective function to solve this blending problem.

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 of the following set of inequalities properly represent the limits on advertisements per week by media?

When formulating transportation LP problems,constraints usually deal with the

A mail order firm,AmazingCo,can use one of 3 shipping couriers.Ajax Shipping charges $6 per pound and delivers in 2 days.Bilco Lanes charges $9 per pound but guarantees next day delivery.The final courier,Hobo Ltd. ,charges only $3 per pound but takes 4 days to deliver.AmazingCo has a quarterly budget of $280,000 and a reputation for timely delivery.Formulate the linear program so that the firm delivers as fast as possible within budget for 70,000 pounds of shipments per quarter.