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Questions and Answers of Statistics

Consider the following four LP formulations. Using a graphical approach, determine(a) Which formulation has more than one optimal solution.(b) Which formulation is unbounded.(c) Which formulation has
Graph the following LP problem and indicate the optimal solution point:Maximize profit = $3X + $2Y Subject to 2X + Y ≤ 150 2X + 3Y ≤ 300(a) Does the optimal solution change if
Graphically analyze the following problem:Maximize profit = $4X + $6YSubject to X + 2Y ≤ 8 hours6X + 4Y ≤ 24 hours(a) What is the optimal solution?(b) If the first constraint is altered to X + 3Y
Examine the LP formulation in Problem 7-29. The problem’s second constraint reads6X + 4Y ≤ 24 hours (time available on machine 2)If the firm decides that 36 hours of time can be made available
Consider the following LP problem:Maximize profit = 5X + 6YSubject to 2X + Y ≤ 1202X + 3Y ≤ 240X, Y ≥ 0(a) What is the optimal solution to this problem? Solve it graphically.(b) If a technical
Consider the LP formulation given in Problem 7-31. If the second constraint is changed from 2X + 3Y ≤ 240 to 2X + 4Y ≤ 240, what effect will this have on the optimal solution?
The computer output given below is for Problem 7-31. Use this to answer the following questions.(a) How much could the profit on X increase or decrease without changing the values of X and Y in the
The computer output on the next page is for a product mix problem in which there are two products and three resource constraints. Use the output to help you answer the following questions. Assume
Graphically solve the following problem:(a) What is the optimal solution?(b) Change the right-hand side of constraint 1 to 11 (instead of 10) and resolve the problem.How much did the profit increase
The three princes of Serendip Went on a little trip.They could not carry too much weight;More than 300 pounds made them hesitate.They planned to the ounce. When they returned to CeylonThey discovered
Bhavika Investments, a group of financial advisors and retirement planners, has been requested to provide advice on how to invest $200,000 for one of its clients. The client has stipulated that the
Refer to the Bhavika Investments (Problem 7-37) situation once again. It has been decided that, rather than minimize risk, the objective should be to maximize return while placing restriction on the
The Feed 'N Ship Ranch fattens cattle for local farmers and ships them to meat markets in Kansas City and Omaha. The owners of the ranch seek to determine the amounts of cattle feed to buy so that
The Weinberger Electronics Corporation manufactures four highly technical products that it supplies to aerospace firms that hold NASA contracts. Each of the products must pass through the following
Outdoor Inn, a camping equipment manufacturer in southern Utah, is developing a production schedule for a popular type of tent, the Double Inn. Orders have been received for 180 of these to be
Outdoors Inn expanded its tent-making operations later in the year. While still making the Double Inn tent, it is also making a larger tent, the Family Rolls, which has four rooms. The company can
Modem Corporation of America (MCA) is the world's largest producer of modem communication devices for microcomputers. MCA sold 9,000 of the regular model and 10,400 of the smart ("intelligent") model
Working with chemists at Virginia Tech and George Washington Universities, landscape contractor Kenneth Golding blended his own fertilizer, called "Golding-Grow." It consists of four chemical
Raptor Fuels produces three grades of gasoline Regular, Premium, and Super. All of these are produced by blending two types of crude oil Crude A and Crude B. The two types of crude contain specific
Ron Garcia felt good about his first week as a management trainee at Mexicana Wire Winding, Inc. He had not yet developed any technical knowledge about the manufacturing process, but he had toured
Winkler Furniture manufactures two different types of china cabinets: a French provincial model and a Danish Modern model. Each cabinet produced must go through three departments: carpentry,
The Heinlein and Krampf Brokerage firm has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of land holdings in Ohio. The client has a
The famous Y. S. Chang Restaurant is open 24 hours a day. Waiters and busboys report for duty at 3 A.M., 7 A.M., 11 A.M., 3 P.M., 7 P.M., or 11 P.M., and each works an 8-hour shift. The following
The Battery Park Stable feeds and houses the horses used to pull tourist-filled carriages through the streets of Charleston's historic waterfront area. The stable owner, an ex-racehorse trainer,
The Kleenglass Corporation makes a dishwasher that has excellent cleaning power. This dishwasher uses less water than most competitors, and it is extremely quiet. Orders have been received from
Eddie Kelly is running for reelection as mayor of a small town in Alabama. Jessica Martinez, Kelly's campaign manager during this election, is planning the marketing campaign, and there is some stiff
The advertising director for Diversey Paint and Supply, a chain of four retail stores on Chicago's North Side, is considering two media possibilities. One plan is for a series of halfpage ads in the
Sundown Rent-a-Car, a large automobile rental agency operating in the Midwest, is preparing a leasing strategy for the next six months. Sundown leases cars from an automobile manufacturer and then
Management of Sundown Rent-a-Car has decided that perhaps the cost during the six-month period is not the appropriate cost to minimize because the agency may still be obligated to additional months
The Arden County, Maryland, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for
The I. Kruger Paint and Wallpaper Store is a large retail distributor of the Supertrex brand of vinyl wall-coverings. Kruger will enhance its citywide image in Miami if it can outsell other local
Kathy Roniger, campus dietitian for a small Idaho college, is responsible for formulating a nutritious meal plan for students.For an evening meal, she feels that the following five meal-content
Quitmeyer Electronics Incorporated manufactures the following six microcomputer peripheral devices: internal modems, external modems, graphics circuit boards, CD drives, hard disk drives, and memory
South Central Utilities has just announced the August 1 opening of its second nuclear generator at its Baton Rouge, Louisiana, nuclear power plant. Its personnel department has been directed to
Margaret Black's family owns five parcels of farmland broken into a southeast sector, north sector, northwest sector, west sector, and southwest sector. Margaret is involved primarily in growing
Amalgamated Products has just received a contract to construct steel body frames for automobiles that are to be produced at the new Japanese factory in Tennessee. The Japanese auto manufacturer has
Refer to Problem 8-16. Find the cause of the difficulty and recommend how to adjust it. Then solve the problem again.
Mt. Sinai Hospital in New Orleans is a large, private, 600-bed facility, complete with laboratories, operating rooms, and x-ray equipment. In seeking to increase revenues, Mt. Sinai's administration
Prepare a written report to the CEO of Mt. Sinai Hospital in Problem 8-18 on the expansion of the hospital. Round off your answers to the nearest integer. The format of presentation of results is
In the Low Knock Oil Company blending problem, it was assumed that one barrel of crude would result in one barrel of gasoline as the final product. In processing one barrel of crude, a typical
Northeast General, a large hospital in Providence, Rhode Island, has initiated a new procedure to ensure that patients receive their meals while the food is still as hot as possible. The hospital
Daniel Grady is the financial advisor for a number of professional athletes. An analysis of the long-term goals for many of these athletes has resulted in a recommendation to purchase stocks with
Coast-to-Coast Airlines is investigating the possibility of reducing the cost of fuel purchases by taking advantage of lower fuel costs in certain cities. Since fuel purchases represent a substantial
The workload in many areas of bank operations has the characteristics of a nonuniform distribution with respect to time of day. For example, at Chase Manhattan Bank in New York, the number of
Compare the similarities and differences of linear and goal programming.
A linear programming problem was developed, and the feasible region was found. If the additional restriction that all variables must be integers were added to the problem, how would the size of the
List the advantages and disadvantages of solving integer programming problems by (a) Rounding off (b) Enumeration.
What is the difference between the three types of integer programming problems? Which do you think is most common, and why?
What is meant by "satisficing," and why is the term often used in conjunction with goal programming?
If you were the president of the college you are attending and were employing goal programming to assist in decision making, what might your goals be? What kinds of constraints would you include in
What does it mean to rank goals in goal programming? How does this affect the problem's solution?
Which of the following are NLP problems, and why?(a) Maximize profit = 3X1 + 5X2 + 99X3Subject to X1 ≥ 10 X2 ≤ 5 X3 ≥ 18(b) Maximize cost = 25X1 + 30X2 + 8X1 X2Subject to X1 ≥ 8 X1 + X2
Elizabeth Bailey is the owner and general manager of Princess Brides, which provides a wedding planning service in Southwest Louisiana. She uses radio advertising to market her business. Two types of
A group of college students is planning a camping trip during the upcoming break. The group must hike several miles through the woods to get to the campsite, and anything that is needed on this trip
Student Enterprises sells two sizes of wall posters, a large 3- by 4-foot poster and a smaller 2- by 3-foot poster. The profit earned from the sale of each large poster is $3; each smaller poster
An airline owns an aging fleet of Boeing 737 jet airplanes.It is considering a major purchase of up to 17 new Boeing model 757 and 767 jets. The decision must take into account numerous cost and
Trapeze Investments is a venture capital firm that is currently evaluating six different investment opportunities. There is not sufficient capital to invest in all of these, but more than one will be
Horizon Wireless, a cellular telephone company, is expanding into a new era. Relay towers are necessary to provide wireless telephone coverage to the different areas of the city. A grid is
Innis Construction Company specializes in building moderately priced homes in Cincinnati, Ohio. Tom Innis has identified eight potential locations to construct new single-family dwellings, but he
A real estate developer is considering three possible projects: a small apartment complex, a small shopping center, and a mini-warehouse. Each of these requires different funding over the next two
Refer to the real estate investment situation in Problem 10-17.(a) Suppose that the shopping center and the apartment would be on adjacent properties, and the shopping center would only be considered
Triangle Utilities provides electricity for three cities. The company has four electric generators that are used to provide electricity. The main generator operates 24 hours per day, with an
The campaign manager for a politician who is running for reelection to a political office is planning the campaign. Four ways to advertise have been selected: TV ads, radio ads, billboards, and
Geraldine Shawhan is president of Shawhan File Works, a firm that manufactures two types of metal file cabinets. The demand for her two-drawer model is up to 600 cabinets per week; demand for a
Solve Problem 10-21. Are any goals unachieved in this solution? Explain.
Hilliard Electronics produces specially coded computer chips for laser surgery in 64MB, 256MB, and 512MB sizes. (1MB means that the chip holds 1 million bytes of information.) To produce a 64MB chip
An Oklahoma manufacturer makes two products: speaker telephones (X1) and pushbutton telephones (X2). The following goal programming model has been formulated to find the number of each to produce
Major Bill Bligh, director of the Army War College's new 6-month attaché training program, is concerned about how the 20 officers taking the course spend their precious time while in his
Mick Garcia, a certified financial planner (CFP) has been asked by a client to invest $250,000. This money may be placed in stocks, bonds, or a mutual fund in real estate. The expected return on
Hinkel Rotary Engine, Ltd., produces four- and sixcylinder models of automobile engines. The firm's profit for each four-cylinder engine sold during its quarterly production cycle is $1,800 –
Motorcross of Wisconsin produces two models of snowmobiles, the XJ6 and the XJ8. In any given production-planning week Motorcross has 40 hours available in its final testing bay. Each XJ6 requires 1
During the busiest season of the year, Green-Gro Fertilizer produces two types of fertilizers. The standard type (X) is just fertilizer, and the other type (Y) is a special fertilizer and weed-killer
Pat McCormack, a financial advisor for Investors R Us, is evaluating two stocks in a particular industry. He wants to minimize the variance of a portfolio consisting of these two stocks, but he wants
Summertime Tees sells two very popular styles of embroidered shirts in southern Florida: a tank top and a regular T-shirt. The cost of the tank top is $6, and the cost of the T-shirt is $8. The
The integer programming problem in the box below has been developed to help First National Bank decide where, out of 10 possible sites, to locate four new branch offices: where Xi represents Winter
In Solved Problem 10-3, nonlinear programming was used to find the best value for the smoothing constant, ( in an exponential smoothing forecasting problem. To see how much the MAD can vary due to
Using the data in Solved Problem 10-3, develop a spreadsheet for a 2-period weighted moving average forecast with weights of 0.6 (w1) for the most recent period and 0.4 (w2) for the other period.
Schank Marketing Research has just signed contracts to conduct studies for four clients. At present, three project managers are free for assignment to the tasks. Although all are capable of handling
The Oakton River had long been considered an impediment to the development of a certain medium-sized metropolitan area in the southeast. Lying to the east of the city, the river made it difficult for
Is the transportation model an example of decision making under certainty or decision making under uncertainty? Why?
Explain how to determine the number of variables and constraints that would be in a transportation problem simply by knowing the number of sources and the number of destinations.
What is a balanced transportation problem? Describe the approach you would use to solve an unbalanced problem.
The stepping-stone method is being used to solve a transportation problem. There is only one empty cell having a negative improvement index, and this index is – 2. The stepping-stone path for this
Explain what happens when the solution to a transportation problem does not have m + n – 1 occupied squares (where m = number of rows in the table and n = number of columns in the table).
What is the enumeration approach to solving assignment problems? Is it a practical way to solve a 5 row × 5 column problem? a 7 × 7 problem? Why?
How could an assignment problem be solved using the transportation approach? What condition will make the solution of this problem difficult?
You are the plant supervisor and are responsible for scheduling workers to jobs on hand. After estimating the cost of assigning each of five available workers in your plant to five projects that must
Sue Simmons's marketing research firm has local representatives in all but five states. She decides to expand to cover the whole United States by transferring five experienced volunteers from their
The management of the Executive Furniture Corporation decided to expand the production capacity at its Des Moines factory and to cut back production at its other factories. It also recognizes a
Formulate the transportation problem in Problem 9-11 as a linear program and solve using computersoftware.
The Hardrock Concrete Company has plants in three locations and is currently working on three major construction projects, each located at a different site.The shipping cost per truckload of
Hardrock Concrete's owner has decided to increase the capacity at his smallest plant. Instead of producing 30 loads of concrete per day at plant 3, that plant's capacity is doubled to 60 loads. Find
Formulate the Hardrock Concrete Company transportation problem in Problem 9-13 as a linear program and solve using computer software. What would change in the linear program if the change in Problem
The Saussy Lumber Company ships pine flooring to three building supply houses from its mills in Pineville, Oak Ridge, and Mapletown. Determine the best transportation schedule for the data given in
The Krampf Lines Railway Company specializes in coal handling. On Friday, April 13, Krampf had empty cars at the following towns in the quantities indicated:TOWN SUPPLY OF CARSMorgantown
Formulate the Krampf Lines Railway Company situation (Problem 9-17) as a linear program and solve using computer software.
An air conditioning manufacturer produces room air conditioners at plants in Houston, Phoenix, and Memphis. These are sent to regional distributors in Dallas, Atlanta, and Denver. The shipping costs
Formulate the air conditioning situation present in Problem 9-18 as a linear program and solve using computer software.
Finnish Furniture manufactures tables in facilities located in three cities-Reno, Denver, and Pittsburgh. The tables are then shipped to three retail stores located in Phoenix, Cleveland, and
Finnish Furniture has experienced a decrease in the demand for tables in Chicago; the demand has fallen to 150 units. What special condition would exist? What is the minimum-cost solution? Will there

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