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Introduction to Management Science 11th Edition Bernard W. Taylor - Solutions

Solve the linear programming model formulated in Problem 19 for the Bradley family farm graphically.a. How many acres of farmland will not be cultivated at the optimal solution? Do the Bradleys use the entire 100-acre tobacco allotment?b. What would the profit for corn have to be for the Bradleys
Solve the linear programming model formulated in Problem 19 for the Bradley farm by using the computer.a. The Bradleys have an opportunity to lease some extra land from a neighbor. The neighbor is offering the land to them for $110 per acre. Should the Bradleys lease the land at that price?What is
The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers. The two types of biscuits require the following resources:The franchise has 6 hours of labor available each morning. The manager has a contract
Solve the linear programming model formulated in Problem 22 for the Burger Doodle restaurant graphically.a. How much extra sausage and ham is left over at the optimal solution point? Is there any idle labor time?b. What would the solution be if the profit for a ham biscuit were increased from $0.50
Solve the linear programming model developed in Problem 22 for the Burger Doodle restaurant by using the computer.a. Identify and explain the shadow prices for each of the resource constraints.b. Which of the resources constraints profit the most?c. Identify the sensitivity ranges for the profit of
Rucklehouse Public Relations has been contracted to do a survey following an election primary in New Hampshire. The firm must assign interviewers to conduct the survey by telephone or in person. One person can conduct 80 telephone interviews or 40 personal interviews in a single day. The following
Solve the linear programming model formulated in Problem 25 for Rucklehouse Public Relations graphically.a. Determine the sensitivity ranges for the daily cost of a telephone interviewer and the number of personal interviews required.b. Does the firm conduct any more telephone and personal
Solve the linear programming model formulated in Problem 25 for Rucklehouse Public Relations by using the computer.a. If the firm could reduce the minimum interview requirement for either telephone or personal interviews, which should the firm select? How much would a reduction of one interview in
The Bluegrass Distillery produces custom-blended whiskey. A particular blend consists of rye and bourbon whiskey. The company has received an order for a minimum of 400 gallons of the custom blend. The customer specified that the order must contain at least 40% rye and not more than 250 gallons of
Solve the linear programming model formulated in Problem 28 for the Bluegrass Distillery graphically.a. Indicate the slack and surplus available at the optimal solution point and explain their meanings.b. What increase in the objective function coefficients in this model would change the optimal
Solve the linear programming model formulated in Problem 28 for the Bluegrass Distillery by using the computer.a. Identify the sensitivity ranges for the objective function coefficients and explain what the upper and lower limits are.b. How much would it be worth to the distillery to obtain
Prissy Pauline’s Barbecue Restaurant in Greensboro makes two primary food items fresh each morning: pulled pork barbecue and beef brisket barbecue. These two items are sold as part of different menu items, including sandwich and barbecue plates, with a variety of different sides. The maximum
Solve the linear programming model formulated in Problem 31 for Prissy Pauline’s Barbecue Restaurant using the computer.a. If the restaurant could get additional pork or beef from the meat supplier, which should it get? Why?b. If the restaurant orders 10 more pounds of beef from its supplier, how
Xara Stores in the United States stocks a particular type of designer denim jeans that is manufactured in China and Brazil and imported to the Xara distribution center in the United States. It orders 500 pairs of jeans each month from its two suppliers. The Chinese supplier charges Xara $11 per
Solve the linear programming model formulated in Problem 33 for Xara Stores graphically and by using the computer.a. If the Chinese supplier were able to reduce its percentage of defective pairs of jeans from 7% to 5%, what would be the effect on the solution?b. If Xara Stores decided to minimize
Alexis Harrington received an inheritance of $95,000, and she is considering two speculative investments—the purchase of land and the purchase of cattle. Each investment would be for 1 year. Under the present (normal) economic conditions, each dollar invested in land will return the principal
Solve the linear programming model formulated in Problem 35 for Alexis Harrington graphically.a. How much would the return for cattle have to increase in order for Alexis to invest only in cattle?b. Should all of Alexis’s inheritance be invested according to the optimal solution?c. How much
Solve the linear programming model formulated in Problem 35 for Alexis Harrington by using the computer.a. If Alexis decided to invest some of her own savings along with the money from her inheritance, what return would she realize for each dollar of her own money that she invested? How much of her
Transform the following linear programming model into standard form and solve by using the computer:Maximize Z = 140x1 + 205x2 + 190x3Subject to10x1 + 15x2 + 8x3 ≤ 610x1 / x2 ≤ 3x1 ≥ 0.4(x1 + x2 + x3)x2 ≥ x3x1, x2, x3 ≥ 0
Chemco Corporation produces a chemical mixture for a specific customer in 1,000-pound batches. The mixture contains three ingredients—zinc, mercury, and potassium. The mixture must conform to formula specifications that are supplied by the customer. The company wants to know the amount of each
The following linear programming model formulation is used for the production of four different products, with two different manufacturing processes and two different material requirements:a. Solve this problem by using the computer.b. Identify the sensitivity ranges for the objective function
Island Publishing Company publishes two types of magazines on a monthly basis: a restaurant and entertainment guide and a real estate guide. The company distributes the magazines free to businesses, hotels, and stores on Hilton Head Island in South Carolina. The company’s profits come exclusively
Solve the linear programming model formulation in Problem 41 for Island Publishing Company graphically.a. Determine the sensitivity range for the advertising revenue generated by the real estate guide.b. Does the company spend all of its printing budget? If not, how much slack is left over?c. What
Solve the linear programming model formulated in Problem 41 for Island Publishing Company by using the computer.a. How much would it be worth to Island Publishing Company to obtain enough additional rack space to distribute 18,500 copies instead of the current 18,000 copies? 20,000 copies?b. How
Mega-Mart, a discount store chain, is to build a new store in Rock Springs. The parcel of land the company has purchased is large enough to accommodate a store with 140,000 square feet of floor space. Based on marketing and demographic surveys of the area and historical data from its other stores,
a. In Problem 44, Mega-Mart is considering purchasing a parcel of land adjacent to the current site on which it plans to build its store. The cost of the parcel is $190,000, and it would enable Mega-Mart to increase the size of its store to 160,000 square feet. Discuss whether Mega Mart should
The Food Max grocery store sells three brands of milk in half-gallon cartons-its own brand, a local dairy brand, and a national brand. The profit from its own brand is $0.97 per carton, the profit from the local dairy brand is $0.83 per carton, and the profit from the national brand is $0.69 per
a. If Food Max in Problem 46 could increase its shelf space for half-gallon cartons of milk, how much would profit increase per carton?b. If Food Max could get the local dairy to increase the amount of milk it could supply each week, would it increase profit?c. Food Max is considering discounting
John Hoke owns Hoke’s Spokes, a bicycle shop. Most of John’s bicycle sales are customer orders; however, he also stocks bicycles for walk-in customers. He stocks three types of bicycles—road-racing, cross-country, and mountain. A road-racing bike costs $1,200, a cross-country bike costs
Solve the linear programming model formulated in Problem 48 for Hoke’s Spokes by using the computer.a. Should John Hoke try to increase his budget for purchasing bikes, increase space to stock bikes, or increase labor hours to assemble bikes? Why?b. If John hired an additional worker for 30 hours
Metro Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches—ham and cheese, bologna, and chicken salad. A ham and cheese sandwich requires a worker 0.45 minutes to assemble, a bologna sandwich requires
Solve the linear programming model formulated in Problem 50 for Metro Food Services Company by using the computer.a. If Metro Food Services could hire another worker and increase its available assembly time by 480 minutes or increase its vending machine capacity by 100 sandwiches, which should it
Mountain Laurel Vineyards produces three kinds of wine—Mountain Blanc, Mountain Red, and Mountain Blush. The company has 17 tons of grapes available to produce wine this season. A cask of Blanc requires 0.21 ton of grapes, a cask of Red requires 0.24 ton, and a cask of Blush requires 0.18 ton.
Solve the linear programming model formulated in Problem 52 for Mountain Laurel Vineyards by using the computer.a. If the vineyard determined that the profit from Red was $7,600 instead of $8,200, how would that affect the optimal solution?b. If the vineyard could secure one additional unit of any
Exeter Mines produces iron ore at four different mines; however, the ores extracted at each mine are different in their iron content. Mine 1 produces magnetite ore, which has a 70% iron content; mine 2 produces limonite ore, which has a 60% iron content; mine 3 produces pyrite ore, which has a 50%
Solve the linear programming model formulated in Problem 54 for Exeter Mines by using the computer.a. Do any of the mines have slack capacity? If yes, which one(s)?b. If Exeter Mines could increase production capacity at any one of its mines, which should it be? Why?c. If Exeter decided to increase
Given the following linear programming model:transform the model into standard form and solve by using thecomputer.
Tracy McCoy has committed to the local PTA to make some items for a bake sale on Saturday. She has decided to make some combination of chocolate cakes, loaves of white bread, custard pies, and sugar cookies. Thursday evening she goes to the store and purchases 20 pounds of flour, 10 pounds of
Solve the linear programming model formulated in Problem 57 for Tracy McCoy.a. Are any of the ingredients left over?b. If Tracy could get more of any ingredient, which should it be? Why?c. If Tracy could get 6 more eggs, 20 more cups of flour, or 30 more minutes of oven time, which should she
The Wisham family lives on a farm in South Georgia on which it produces a variety of crops and livestock, including pecans. It has 5 acres of pecan trees that yield approximately 1,000 pounds of unshelled pecans per acre each year. The family uses all of its pecan harvest to produce pecan pies,
Solve the linear programming model formulated in Problem 59 for the Wisham family farm using the computer.a. Are there any extra (slack) resources available?b. If the Wisham family could obtain additional resources, which one would be of most value to them? How much would they be willing to pay for
During the winter WeeMow Lawn Service contracts with customers for cutting lawns starting in the spring. WeeMow provides service to residential and commercial customers. The service has identified 50 possible residential customers and 15 potential commercial customers it has contacted. WeeMow
Gilbert Moss and Angela Pasaic spent several summers during their college years working at archaeological sites in the Southwest. While at those digs, they learned how to make ceramic tiles from local artisans. After college they made use of their college experiences to start a tile manufacturing
In "The Possibility" Restaurant case problem in Chapter 2, Angela Fox and Zooey Caulfield opened a French restaurant called "The Possibility." Initially, Angela and Zooey could not offer a full, varied menu, so their chef, Pierre, prepared two full-course dinners with beef and fish each evening. In
Julia Robertson is a senior at Tech, and she's investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game, and Julia knows, from attending the games herself, that everyone
In the product mix example in this chapter, Quick-Screen is considering adding some extra operators who would reduce processing times for each of the four clothing items by 10%. This would also increase the cost of each item by 10% and thus reduce unit profits by this same amount (because an
In the diet example in this chapter, what would be the effect on the optimal solution of increasing the minimum calorie requirement for the breakfast to 500 calories? to 600 calories? Increase the breakfast calorie requirement to 700 calories and reformulate the model to establish upper limits on
In the investment example in this chapter, how would the solution be affected if the requirement that the entire $70,000 be invested was relaxed such that it is the maximum amount available for investment?If the entire amount available for investment does not have to be invested and the amount
For the marketing example in this chapter, if the budget is increased by $20,000, how much will audience exposures be increased?If Biggs Department Store wanted the same total number of people exposed to each of the three types of advertisements, how should the linear programming model be
For the transportation example in this chapter, suppose that television sets not shipped were to incur storage costs of $9 at Cincinnati, $6 at Atlanta, and $7 at Pittsburgh. How would these storage costs be reflected in the linear programming model for this example problem, and what would the new
For the blend example in this chapter, if the requirement that “at least 3,000 barrels of each grade of motor oil” was changed to exactly 3,000 barrels of each grade, how would this affect the optimal solution?If the company could acquire more of one of the three components, which should it be?
On their farm, the Friendly family grows apples that they harvest each fall and make into three products—apple butter, applesauce, and apple jelly. They sell these three items at several local grocery stores, at craft fairs in the region, and at their own Friendly Farm Pumpkin Festival for 2
a. If the Friendlys in Problem 7 were to use leftover apples to feed livestock, at an estimated cost savings worth $0.08 per apple in revenue, how would this affect the model and solution?b. Instead of feeding the leftover apples to the livestock, the Friendlys are thinking about producing apple
A hospital dietitian prepares breakfast menus every morning for the hospital patients. Part of the dietitian€™s responsibility is to make sure that minimum daily requirements for vitamins A and B are met. At the same time, the cost of the menus must be kept as low as possible. The main
Lakeside Boatworks is planning to manufacture three types of molded fiberglass recreational boats€”a fishing (bass) boat, a ski boat, and a small speedboat. The estimated selling price and variable cost for each type of boat are summarized in the following table:The company has incurred
The Pyrotec Company produces three electrical products€”clocks, radios, and toasters. These products have the following resource requirements:The manufacturer has a daily production budget of $2,000 and a maximum of 660 hours of labor.Maximum daily customer demand is for 200 clocks, 300
Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks three brands of beer—Yodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is as follows:Brand ......
The Kalo Fertilizer Company produces two brands of lawn fertilizer€”Super Two and Green Grow€”at plants in Fresno, California, and Dearborn, Michigan. The plant at Fresno has resources available to produce 5,000 pounds of fertilizer daily; the plant at Dearborn has enough
Grafton Metalworks Company produces metal alloys from six different ores it mines. The company has an order from a customer to produce an alloy that contains four metals according to the following specifications: at least 21% of metal A, no more than 12% of metal B, no more than 7% of metal C, and
The Roadnet Transport Company expanded its shipping capacity by purchasing 90 trailer trucks from a bankrupt competitor. The company subsequently located 30 of the purchased trucks at each of its shipping warehouses in Charlotte, Memphis, and Louisville. The company makes shipments from each of
The Hickory Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, North Carolina. The plant uses three main resources to make furniture€”wood, upholstery, and labor. The resource requirements for each piece of furniture and the total resources
Lawns Unlimited is a lawn care and maintenance company. One of its services is to seed new lawns as well as bare or damaged areas in established lawns. The company uses three basic grass seed mixes it calls Home 1, Home 2, and Commercial 3. It uses three kinds of grass seed€”tall fescue,
Alexandra Bergson has subdivided her 2,000-acre farm into three plots and has contracted with three local farm families to operate the plots. She has instructed each sharecropper to plant three crops: corn, peas, and soybeans. The size of each plot has been determined by the capabilities of each
As a result of a recently passed bill, a congressman’s district has been allocated $4 million for programs and projects. It is up to the congressman to decide how to distribute the money. The congressman has decided to allocate the money to four ongoing programs because of their importance to his
Anna Broderick is the dietitian for the State University football team, and she is attempting to determine a nutritious lunch menu for the team. She has set the following nutritional guidelines for each lunch serving:Between 1,500 and 2,000 caloriesAt least 5 mg of ironAt least 20 but no more than
The Midland Tool Shop has four heavy presses it uses to stamp out prefabricated metal covers and housings for electronic consumer products. All four presses operate differently and are of different sizes. Currently the firm has a contract to produce three products. The contract calls for 400 units
The Cabin Creek Coal (CCC) Company operates three mines in Kentucky and West Virginia, and it supplies coal to four utility power plants along the East Coast. The cost of shipping coal from each mine to each plant, the capacity at each of the three mines, and the demand at each plant are shown in
Ampco is a manufacturing company that has a contract to supply a customer with parts from April through September. However, Ampco does not have enough storage space to store the parts during this period, so it needs to lease extra warehouse space during the 6-month period. Following are Ampco’s
Brooks City has three consolidated high schools, each with a capacity of 1,200 students. The school board has partitioned the city into five busing districtsâ€”north, south, east, west, and centralâ€”each with different high school student populations. The three schools are located in the
a. In Problem 24 the school board decided that because all students in the north and east districts must be bused, then at least 50% of the students who live in the south, west, and central districts must also be bused to another district. Reformulate the linear programming model to reflect this
The Southfork Feed Company makes a feed mix from four ingredients—oats, corn, soybeans, and a vitamin supplement. The company has 300 pounds of oats, 400 pounds of corn, 200 pounds of soybeans, and 100 pounds of vitamin supplement available for the mix. The company has the following requirements
The United Charities annual fund-raising drive is scheduled to take place next week. Donations are collected during the day and night, by telephone, and through personal contact. The average donation resulting from each type of contact is as follows:The charity group has enough donated gasoline and
Ronald Thump is interested in expanding his firm. After careful consideration, he has determined three areas in which he might invest additional funds: (1) product research and development, (2) manufacturing operations improvements, and (3) advertising and sales promotion. He has $500,000 available
Iggy Olweski, a professional football player, is retiring, and he is thinking about going into the insurance business. He plans to sell three types of policies—homeowner’s insurance, auto insurance, and life insurance. The average amount of profit returned per year by each type of insurance
A publishing house publishes three weekly magazines€”Daily Life, Agriculture Today, and Surf€™s Up. Publication of one issue of each of the magazines requires the following amounts of production time and paper:Each week the publisher has available 120 hours of production time
The manager of a department store in Seattle is attempting to decide on the types and amounts of advertising the store should use. He has invited representatives from the local radio station, television station, and newspaper to make presentations in which they describe their audiences.The
The Mill Mountain Coffee Shop blends coffee on the premises for its customers. It sells three basic blends in 1-pound bags, Special, Mountain Dark, and Mill Regular. It uses four different types of coffee to produce the blends€”Brazilian, mocha, Colombian, and mild. The shop has the
Toyz is a large discount toy store in Valley Wood Mall. The store typically has slow sales in the summer months that increase dramatically and rise to a peak at Christmas. During the summer and fall, the store must build up its inventory to have enough stock for the Christmas season. To purchase
The Skimmer Boat Company manufactures the Water Skimmer bass fishing boat. The company purchases the engines it installs in its boats from the Mar-gine Company, which specializes in marine engines. Skimmer has the following production schedule for April, May, June, and July:Month .......
The Donnor meat processing firm produces wieners from four ingredients: chicken, beef, pork, and a cereal additive. The firm produces three types of wieners: regular, beef, and all-meat. The company has the following amounts of each ingredient available on a daily basis:Each type of wiener has
Joe Henderson runs a small metal parts shop. The shop contains three machines-a drill press, a lathe, and a grinder. Joe has three operators, each certified to work on all three machines. However, each operator performs better on some machines than on others. The shop has contracted to do a big job
Green Valley Mills produces carpet at plants in St. Louis and Richmond. The plants ship the carpet to two outlets in Chicago and Atlanta. The cost per ton of shipping carpet from each of the two plants to the two warehouses is as follows:The plant at St. Louis can supply 250 tons of carpet per
Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determine a schedule for nurses to make sure there are enough of them on duty throughout the day. During the day, the demand for nurses varies. Maureen has broken the day into twelve 2-hour periods. The slowest
A manufacturer of bathroom fixtures produces fiberglass bathtubs in an assembly operation that consists of three processes—molding, smoothing, and painting. The number of units that can undergo each process in an hour is as follows:Process . Output (units/hr.)Molding ....... 7Smoothing ........
The admissions office at State University wants to develop a planning model for next year€™s entering freshman class. The university has 4,500 available openings for freshmen. Tuition is $8,600 for an in-state student and $19,200 for an out-of-state student. The university wants to
A manufacturing firm located in Chicago ships its product by railroad to Detroit. Several different routes are available, as shown in the following diagram, referred to as a network:Each circle in the network represents a railroad junction. Each arrow is a railroad branch between two junctions. The
A refinery blends four petroleum components into three grades of gasoline€”regular, premium, and diesel. The maximum quantities available of each component and the cost per barrel are as follows:To ensure that each gasoline grade retains certain essential characteristics, the refinery has
Melissa Beadle is a student at Tech, and she wants to decide how many hours each day to allocate to the following activities: class; studying; leisure and fun stuff; personal activities such as eating, bathing, cleaning, laundry, and so on; and sleeping. She has established weights indicating how
Tech, with a student population of 30,000, is located in a small college town in Virginia. Direct Cast Cable TV has a small service staff that is sufficient to handle installations and TV hookups for almost the entire year. However, for the month-long period right before and during the beginning of
The Cash and Carry Building Supply Company has received the following order for boards in three lengths:Length ... Order (quantity)7 ft. ..... 7009 ft. .... 1,20010 ft. ..... 300The company has 25-foot standard-length boards in stock. Therefore, the standard-length boards must be cut into the
An investment firm has $1 million to invest in stocks, bonds, certificates of deposit, and real estate. The firm wishes to determine the mix of investments that will maximize the cash value at the end of 6 years.Opportunities to invest in stocks and bonds will be available at the beginning of each
The Jones, Jones, Smith, and Rodman commodities trading firm knows the prices at which it will be able to buy and sell a certain commodity during the next 4 months. The buying price and selling price (pi) for each of the given months (i) are as follows:The firm€™s warehouse has a maximum
The production manager of Videotechnics Company is attempting to determine the upcoming 5-month production schedule for video recorders. Past production records indicate that 2,000 recorders can be produced per month. An additional 600 recorders can be produced monthly on an overtime basis. Unit
The manager of the Ewing and Barnes Department Store has four employees available to assign to three departments in the store€”lamps, sporting goods, and linens. The manager wants each of these departments to have at least one employee, but not more than two. Therefore, two departments
Managers at the Transcontinent Shipping and Supply Company want to know the maximum tonnage of goods they can transport from city A to city F. The firm can contract for railroad cars on different rail routes linking these cities via several intermediate stations, shown in the following diagram; all
The law firm of Smith, Smith, Smith, and Jones is recruiting at law schools for new lawyers for the coming year. The firm has developed the following estimate of the number of hours of casework it will need its new lawyers to handle each month for the following year:Each new lawyer the firm hires
In Problem 53, the optimal solution results in a fractional (i.e., non-integer) number of lawyers being hired. Explain how you would go about logically determining a new solution with a whole (integer) number of lawyers being hired and discuss the difference in results between this new solution and
The Goliath Tool and Machine Shop produces a single product that consists of three subcomponents that are assembled to form the product. The three components are manufactured in an operation that involves two lathes and three presses. The production time (in minutes per unit) for each machine for
A ship has two cargo holds, one fore and one aft. The fore cargo hold has a weight capacity of 70,000 pounds and a volume capacity of 30,000 cubic feet. The aft hold has a weight capacity of 90,000 pounds and a volume capacity of 40,000 cubic feet. The shipowner has contracted to carry loads of
Eyewitness News is shown on channel 5 Monday through Friday evenings from 5:00 P.M. to 6:00 P.M. During the hour-long broadcast, 18 minutes are allocated to commercials. The remaining 42 minutes of airtime are allocated to single or multiple time segments for local news and features, national news,

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