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Quantitative Analysis For Management 11th Edition Barry Render, Ralph M. Stair, Michael E. Hanna - Solutions

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 no feasible solution.(d) Which formulation is correct asis.
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 the profit per unit of X changes to $4.50?(b) What happens if the profit function should have been $3X
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 ≤ 8, does the feasible region or optimal solution change?
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 on machine 2 (namely, an additional 12 hours) at an additional cost of $10, should it add the hours?
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 breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal
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 optimal solution?(b) If the right-hand side of constraint 1 were increased by 1 unit, how much would
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 that you wish to maximize profit in each case.(a) How many units of product 1 and product 2 should be
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 as a result of this?(c) Change the right-hand side of constraint 1 to 6 (instead of 10) and resolve
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 that their supplies were just about goneWhen, what to their joy, Prince William foundA pile of
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 money must be put into either a stock fund or a money market fund, and the annual return should be at
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 amount of risk. The average risk should be no more than 11 (with a total risk of 2,200,000 for 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 minimum nutritional standards are satisfied, and at the same time total feed costs are minimized. The
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 departments before they are shipped: wiring, drilling, assembly, and inspection. The time requirement
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 delivered at the end of this month, 220 to be delivered at the end of next month, and 240 to be delivered
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 produce up to a combined total of 280 tents per month. The following table provides the demand that
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 this September. Its income statement for the month is shown in the table on this page. Costs
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 compounds, C-30, C-92, D-21, and E-11. The cost per pound for each compound is indicated as
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 ingredients which help in determining the octane rating of gasoline. The important ingredients and
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 the entire facility, located in the suburbs of Mexico City, and had met many people in various areas
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, painting, and finishing. The table below contains all relevant information concerning production times per
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 good deal of trust in the investment house, but she also has her own ideas about the distribution of
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 table shows the minimum number of workers needed during the six periods into which the day is divided.
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, recognizes the need to set a nutritional diet for the horses in his care. At the same time, he would
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 several retails stores for delivery at the end of each of the next 3 months, as shown below:
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 competition. Martinez has selected four ways to advertise: television ads, radio ads, billboards,
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 Sunday Chicago Tribune newspaper, and the other is for advertising time on Chicago TV.The stores are
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 rents them to the public on a daily basis. A forecast of the demand for Sundown's cars in the next six
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 on some leases after that time. For example, if Sundown had some cars delivered at the beginning of
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 several sectors of the county are beyond walking distance to a school. The superintendent partitions
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 stores in total number of rolls of Supertrex next year. It is able to estimate the demand function as
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 requirements should be met:(1) Between 900 and 1,500 calories;(2) At least 4 milligrams of iron;(3) No
Quitmeyer Electronics Incorporated manufactures the following six microcomputer peripheral devices: internal modems, external modems, graphics circuit boards, CD drives, hard disk drives, and memory expansion boards. Each of these technical products requires time, in minutes, on three types of
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 determine how many nuclear technicians need to be hired and trained over the remainder of the year.The
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 wheat, alfalfa, and barley crops and is currently preparing her production plan for next year. The
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 strict quality control standards for all of its component subcontractors and has informed Amalgamated
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 has decided to make a 90 bed addition on a portion of adjacent land currently used for staff
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 important.The CEO is a busy person and wants to be able to find your optimal solution quickly in your
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 gasoline yield is about 0.46 barrels, although it could be higher or lower than this, depending on the
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 will continue to prepare the food in its kitchen but will now deliver it in bulk (not individual
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 some of their income that is set aside for investments. Five stocks have been identified as having very
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 portion of operating expenses for an airline, it is important that these costs be carefully
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 domestic money transfer requests received from customers, if plotted against time of day, would appear to
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 feasible region change? How would the optimal value of the objective function change?
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 your model?
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 ≥ 12 0.0005X1 – X2 = 11(c) Maximize Z = P1d1– + P2d2+ + P3+Subject to X1 + X2 + d1– – d1+ =
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 ads are available-those during prime time hours and those at other times. Each prime time ad costs
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 must be packed in a knapsack and carried to the campsite. One particular student, Tina Shawl, has
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 earns $2. The firm, although profitable, is not large; it consists of one art student, Jan Meising, at
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 capability factors, including the following:(1) The airline can finance up to $1.6 billion in
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 selected. A 0-1 integer programming model is planned to help determine which of the six
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 superimposed on a map of the city to help determine where the towers should be located. The grid consists of 8
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 cannot put up homes on all of the sites because he has only $300,000 to invest in all projects. The
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 years, and the net present value of the investments also varies.The following table provides the
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 if the apartment were also built. Formulate the constraint that would stipulate this.(b) Formulate
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 occasional shutdown for routine maintenance. Three other generators (1, 2, and 3) are available to provide
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 newspaper ads. The cost of these are $900 for each TV ad, $500 for each radio ad, $600 for a billboard
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 threedrawer cabinet is limited to 400 per week. Shawhan File Works has a weekly operating capacity of
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 requires 8 hours of labor, a 256MB chip takes 13 hours, and a 512MB chip requires 16
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 each day to meet the firm€™s goals:Find the optimal solution using acomputer.
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 charge.Major Bligh recognizes that there are 168 hours per week and thinks that his students have been using
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 investment is 13% for stocks, 8% for bonds, and 10% for real estate. While the client would like a very
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 – $50X1, where X1 is the number sold. Hinkel makes $2,400 – $70X2 for each of the larger engines sold,
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 hour to test and each XJ8 takes 2 hours. The revenue (in $1,000s) for the firm is nonlinear and is
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 combination. The following model has been developed to determine how much of each type should be
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 to have an expected return of at least 9%. After obtaining historical data on the variance and
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 demand for these is sensitive to the price, and historical data indicate that the weekly demands are
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 Park, Maitland, Osceola, Downtown, South Orlando, Airport, Winter Garden, Apopka, Lake Mary, Cocoa
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 the selection of the smoothing constant, use Excel and the data in Program 10.13A to find the value of
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. Note these weights sum to 1, so the forecast is simplyForecast for next period = w1 (Value in current
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 each assignment the times and costs to complete the studies depend on the experience and knowledge
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 people living on its eastern bank to commute to jobs in and around the city and to take advantage
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 cell indicates that the smallest quantity for the cells with minus signs is 80 units. If the total
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 be completed immediately, you solve the problem using the Hungarian method. The following solution
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 current locations to new offices in each of the five states. Simmons's goal is to relocate the five
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 shifting market for its desks and revises the requirements at its three warehouses.(a) Use the northwest
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 concrete, daily plant capacities, and daily project requirements are provided in the table below.(a)
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 the new optimal solution using the northwest corner rule and stepping-stone method. How has changing
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 9-14 were implemented?
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 table. Use the northwest corner rule and the stepping stone method.
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 ......... 35Youngstown ......... 60Pittsburgh ........... 25By Monday, April 16, the following towns will
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 vary, and the company would like to find the least-cost way to meet the demands at each of the
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 Chicago. Management wishes to develop a distribution schedule that will meet the demands at the lowest
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 be any units remaining at any of the manufacturing facilities?

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