Question: CareMed, an HMO health care provider, operates
CareMed, an HMO health care provider, operates a 24-hour outpatient clinic in Draperton, near the Tech campus. The facility has a medical staff with doctors and nurses who see regular local patients according to a daily appointment schedule. However, the clinic sees a number of Tech students, who visit the clinic each day and evening without appointments because their families are part of the CareMed network. The clinic has 12 nurses who work according to three 8-hour shifts. Five nurses are needed from 8:00 A.M. to 4:00 p.M., four nurses work from 4:00 p.M. to midnight, and 3 nurses work overnight from midnight to 8:00 A.M. The clinic administrator wants to assign nurses to a shift according to their preferences and seniority (i.e., when the number of nurses who prefer a shift exceeds the shift demand, the nurses are assigned according to seniority). Although the majority of nurses prefer the day shift, some prefer other shifts because of the work and school schedules of their spouses and families. Following are the nurses’ shift preferences (where 1 is most preferred) and their years working at the clinic:
Formulate and solve a linear programming model to assign the nurses to shifts according to their preferences and seniority.
> Ed Norris has developed a Web site for his used textbook business at State University. To sell advertising, he needs to forecast the number of site visits he expects in the future. For the past 6 months he has had the following number of site visits: D
> A car manufacturing company has its manufacturing plants in Chennai and Mumbai in India. The company transports its cars from these manufacturing plants to its distribution centers located in Bangalore and Hyderabad to meet the demands. Currently, the Mu
> A university student, Benny Orsini, is planning to open a walk-in pizza restaurant near campus that he will call Benny’s Big Slice Pizza. He will have limited seating and will sell two kinds of oversized slices of pizza to go, plain cheese and pepperoni.
> Maria Eagle is a Native American artisan. She works part-time making bowls and mugs by hand from special pottery clay and then sells her items to the Beaver Creek Pottery Company, a Native American crafts guild. She has 60 hours available each month to m
> Consider a model in which two products, x and y, are produced. There are 100 pounds of material and 80 hours of labor available. It requires 2 pounds of material and 1 hour of labor to produce a unit of x, and 4 pounds of material and 5 hours of labor to
> In the example used to demonstrate model construction in this chapter, a firm sells a product, x, for $20 that costs $5 to make, it has 100 pounds of steel to make the product, and it takes 4 pounds of steel to make each unit. The model that was construc
> In Problem 33, Annie has used historical weather data to determine that next season there is a 60% chance that the weather will be good and a 40% chance the weather will be bad. Given this additional information, what do you think Annie’s decision should
> Although Annie Russell (in problem 22) has been told by the athletic department at Tech that all the games will likely be sellouts, she is aware that the weather will affect how many fans will actually attend the games and buy hot dogs. Fans are less lik
> WeeMow Lawn Service provides lawn service, including mowing lawns and lawn care, landscaping, and lawn maintenance, to residential and commercial customers in the Draper town community. In the summer WeeMow has three teams that it schedules daily for job
> Erken Apparel International manufactures clothing items around the world. It has currently contracted with a U.S. retail clothing wholesale distributor for men’s goatskin and lambskin leather jackets for the next Christmas season. The d
> Each spring the Tech Student Government Association (SGA) organizes an event called “Give-Back Weekends.” The SGA solicits student teams to work on projects for residents in the university community on four consecutive
> Jim Huang and Roderick Wheeler were sales representatives in a computer store at a shopping mall in Arlington, Virginia, when they got the idea of going into business in the burgeoning and highly competitive microcomputer market. Jim went to Taiwan over
> The Graphic Palette is a firm in Charleston, South Carolina, that does graphic artwork and produces color and black-and- white posters, lithographs, and banners. The firm’s owners, Kathleen and Lindsey Taylor, have been approached by a
> Kim Davis has decided to purchase a cellular phone, but she is unsure about which rate plan to select. The “regular” plan charges a fixed fee of $55 per month for 1,000 minutes of airtime plus $0.33 per minute for any time over 1,000 minutes. The “execut
> Brenda Last is the personnel director at the Burlingham Textile Company. The company’s plant is expanding, and Brenda must fill five new supervisory positions in carding, spinning, weaving, inspection, and shipping. Applicants for the p
> Rachel Sundusky is the manager of the South-Atlantic office of the Stateline Shipping and Transport Company. She is in the process of negotiating a new shipping contract with Polychem, a company that manufactures chemicals for industrial use. Polychem wa
> The management science and information technology department at Tech offers between 36 and 40 three-hour course sections each semester. Some of the courses are taught by graduate student instructors, whereas 20 of the course sections are taught by the 10
> Chuck and his daughter Kathleen want to go on a trip in July to visit as many major league baseball parks for games as they can during Chuck’s week-long vacation from work. They would like to visit as many of the newer ball- parks as they can, but they a
> Kathleen Taylor has been working for a government contractor, Summit Solutions, in Washington, DC, for over a year. She is now eligible to participate in the company’s 401(k) retirement plan. The company has provided Kathleen with the i
> The Lead Balloon is a popular ’80s rock band that broke up in the 1990s but recently got back together to publish a new CD and go on tour. They want to schedule a summer tour that will encompass 16 possible cities in the eastern half of
> All students in the College of Business at State University are required to take a capstone course, Management 4394, the last semester of their senior year. This course consists primarily of a semester-long case project that pulls together all the busine
> Each fall the Draperton Parks and Recreation Department holds a series of tryouts for its boys’ and girls’ youth basketball leagues. All leagues are formed by age group, all girls who try out are placed on teams; some
> The United Broadcast Network (UBN) sells to advertisers commercial advertising slots on its television shows. The network announces its new fall television schedule during the previous spring and shortly thereafter begins selling its inventory of adverti
> Atlantic Management Systems is a consulting firm that specializes in developing computerized decision support systems for computer manufacturing companies. The fir currently has offices in Chicago, Charlotte, Pittsburgh, and Houston. It is considering op
> The General Store at State University is an auxiliary bookstore located near the dormitories that sells academic supplies, toiletries, sweatshirts and T-shirts, magazines, packaged food items, and canned soft drinks and fruit drinks. The manager of the s
> The Tennessee Pterodactyls is a new professional basket- ball franchise in Nashville. The team’s general manager, Jerry East, and coach, Phil Riley, are trying to develop a roster of players. They drafted seven players from a pool to wh
> Paulette Smith and Maureen Becker are seniors in engineering and business, respectively, at State University. They have set up a company, PM Computer Services, to assemble and sell their own brand of personal computers. They buy component parts on the op
> If Evergreen Fertilizer Company increases its advertising expenditures by $14,000 per year, what effect will the increase have on the break-even volume computed in Problem 13?
> If Evergreen Fertilizer Company changes its production process to add a weed killer to the fertilizer to increase sales, the variable cost per pound will increase from $0.15 to $0.22. What effect will this change have on the break-even volume computed in
> If Evergreen Fertilizer Company in Problem 4 changes the price of its fertilizer from $0.40 per pound to $0.60 per pound, what effect will the change have on the break-even volume?
> If the Gobblecakes bakery in Problem 2 changes the selling price for a cupcake from $3.20 to $2.75, what effect will the change have on the break-even volume?
> King’s Landing is a large amusement theme park located in Virginia. The park hires high school and college students to work during the summer months of May, June, July, August, and September. The student employees operate virtually all the highly mechani
> If the maximum operating capacity of Evergreen Fertilizer Company described in Problem 4 is 120,000 pounds of fertilizer per month, determine the break-even volume as a percentage of capacity.
> If the maximum operating capacity of the Rolling Creek Textile Mill described in Problem 3 is 25,000 yards of denim per month, determine the break-even volume as a percentage of capacity.
> If the maximum operating capacity of the Gobblecakes bakery described in Problem 2 is 12,000 cupcakes annually, determine the break-even volume as a percentage of that capacity.
> Andy Mendoza makes handcrafted dolls, which he sells at craft fairs. He is considering mass- producing the dolls to sell in stores. He estimates that the initial investment for plant and equipment will be $25,000, whereas labor, material, packaging, and
> Graphically illustrate the break-even volume for the Evergreen Fertilizer Company determined in Problem 4.
> Graphically illustrate the break-even volume for the Gobblecakes bakery determined in Problem 2.
> Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is $25,000, and its variable cost per pound of fertilizer is $0.15. Evergreen sells the fertilizer for $0.40 per pound. Determine the monthly break-even volume for the com
> The Rolling Creek Textile Mill produces denim. The fixed monthly cost is $21,000, and the variable cost per yard of denim is $0.45. The mill sells a yard of denim for $1.30. a. For a monthly volume of 18,000 yards of denim, determine the total cost, tota
> Coca-Cola Great Britain offers more than 80 drinks across 20 different brands. The company distributes its drinks to four regions—West Midlands, East Midlands, South East, and South West — from its bottling plants at Y
> The Interstate Truck Rental firm has accumulated extra trucks at three of its truck leasing outlets, as shown in the following table: The firm also has four outlets with shortages of rental trucks, as follows: The firm wants to transfer trucks from those
> Walsh’s Juice Company produces three products from unprocessed grape juice—bottled juice, frozen juice con- centrate, and jelly. It purchases grape juice from three vineyards near the Great Lakes. The grapes are harves
> A tire manufacturer supplies tires to three vehicle manufacturers—Hyundai, Honda, and Toyota. Vehicle manufacturers buy tires for their cars in multiples of five from the different plants as four tires are assembled with each car and on
> The National Collegiate Lacrosse Association is planning its annual national championship tournament. It selects 16 teams from conference champions and the highest ranked at-large teams to play in the single-elimination tournament. The teams are ranked f
> The Hilton Island Tennis Club is hosting its annual professional tennis tournament. One of the tournament committee’s scheduling activities is to assign chair umpires to the various matches. The tennis association rates chair umpires fr
> Refer to the data given in Problem 60 and assume that one salesman should be assigned to only one zone. a. Determine the optimal assignment. b. What is the effect on the expected revenue?
> A company wants to assign ten salesmen to eight different sales zones. The expected profit from each salesman differs from one zone to another based on their experience with the different customers in the respective zone. The company needs at least one s
> Onions are considered an indispensable ingredient in most of Indian cooking. Maximum onion production takes place in the state of Maharashtra (4.90 million tons) followed by Karnataka (2.59 million tons), Gujarat (2.65 million tons), and Bihar (1.08 mill
> Kathleen Taylor is a freshman at Roanoke College, and she wants to develop her schedule for the spring semester. Courses are offered with class periods either on Monday and Wednesday or Tuesday and Thursday for 1 hour and 15 minutes duration, with 15 min
> A travel company in Dubai owns four passenger cars with different seating capacities. The profit per trip depends on several factors like the season of the year, tourist requirements, the time of the day the trip starts, and the duration tourists want to
> A mobile manufacturer must produce five types of microprocessors. Currently five work centers are available for production. Each work center can produce each type of microprocessor; however, the time required to produce a unit at a work center differs de
> After Susan Wong graduated from State University with a degree in management science, she went to work for a computer systems development firm in the Washington, DC, area. As a student at State, Susan paid her normal monthly living expenses for apart
> The Vanguard Publishing Company wants to hire seven of the eight college students who have applied as salespeople to sell encyclopedias during the summer. The company desires to allocate them to three sales territories. Territory 1 requires three salespe
> Biggio’s Department Store has six employees available to assign to four departments in the store— home furnishings, china, appliances, and jewelry. Most of the six employees have worked in each of the four departments
> The coach of the women’s swim team at State University is preparing for the conference swim meet and must choose the four swimmers she will assign to the 800-meter medley relay team. The medley relay consists of four strokesâ€
> A university department head has five instructors to be assigned to four different courses. All the instructors have taught the courses in the past and have been evaluated by the students. The rating for each instructor for each course is given in the fo
> State University has planned six special catered events for the Saturday of its homecoming football game. The events include an alumni brunch, a parents’ brunch, a booster club luncheon, a postgame party for season ticket holders, a let
> In Problem 49, officials 2 and 8 recently had a confrontation with one of the coaches in the game in Athens. They were forced to eject the coach after several technical fouls. The conference office decided that it would not be a good idea to have these t
> South Africa is one of the largest coal producing and exporting countries in the world. A company dealing with coal sources coal from four coalfields—Highveld, Emalehleni, Ermelo, and Klip River. The capacities of the four coalfields ar
> The Southeastern Conference has nine basketball officials who must be assigned to three conference games, three to each game. The conference office wants to assign the officials so that the total distance they travel will be minimized. The distance (in m
> A dispatcher for Citywide Taxi Company has six taxicabs at different locations and five customers who have called for service. The mileage from each taxi’s present location to each customer is shown in the following table: Determine the
> An electronics firm produces electronic components, which it supplies to various electrical manufacturers. Quality control records indicate that different employees produce different numbers of defective items. The average number of defects produced by e
> The Spring family has owned and operated a garden tool and implements manufacturing company since 1952. The company sells garden tools to distributors and also directly to hardware stores and home improvement discount chains. The Spring Companyâ
> Given the following cost table for an assignment problem, determine the optimal assignment and compute total minimum cost:
> The Bunker Manufacturing firm has five employees and six machines and wants to assign the employees to the machines to minimize cost. A cost table showing the cost incurred by each employee on each machine follows: Because of union rules regarding depart
> The Omega pharmaceutical firm has five salespersons, whom the firm wants to assign to five sales regions. Given their various previous contacts, the salespersons are able to cover the regions in different amounts of time. The amount of time (days) requir
> A shop has four machinists to be assigned to four machines. The hourly cost of having each machine operated by each machinist is as follows: However, because he does not have enough experience, machinist 3 cannot operate machine B. a. Determine the optim
> A plant has four operators to be assigned to four machines. The time (minutes) required by each worker to produce a product on each machine is shown in the following table: Determine the optimal assignment and compute total minimum time.
> Solve problem 32 from Chapter 4 using the computer.
> Formulate and solve a transshipment model for the shipments of cottons from the cotton processing facilities to the U.S. ports and to the overseas ports and Suntrek’s fabric factories as described in Problems 20 and 21.
> Steel mills in three cities produce the following amounts of steel: These mills supply steel to four cities, where manufacturing plants have the following demand: Shipping costs per ton of steel are as follows: Because of a truckers’ st
> The Pinnacle Company is a U.S.-based manufacturer of furniture and appliances that offshored all of its actual manufacturing operations to Asia about a decade ago. It then set up distribution centers at various locations on the East Coast, near ports whe
> Blue Mountain Coffee Company produces various blends of Free Trade, organic specialty coffees that it sells to wholesale customers. The company imports 25 million pounds of coffee beans annually from coffee plantations in Brazil, Indonesia, Kenya, Colomb
> Mary Kelly is a scholarship soccer player at State University. During the summer, she works at a youth all-sports camp that several of the university’s coaches operate. The sports camp runs for 8 weeks during July and August. Campers co
> In Problem 36, KanTech Corporation is just as concerned that its U.S. distributors receive shipments in the minimum amount of time as they are about minimizing their shipping costs. Suppose that each U.S. distributor receives one major container shipment
> KanTech Corporation is a global distributor of electrical parts and components. Its customers are electronics companies in the United States, including computer manufacturers and audio/visual product manufacturers. The company contracts to purchase compo
> A mango-processing unit produces mango juice only during the four months mangoes are harvested. The following diagram shows the production capacities in liters, demand for juice in liters, production cost per liter of juice in rupees shown above the arro
> Horizon Computers manufactures laptops in Germany, Belgium, and Italy. Because of high tariffs between international trade groups, it is sometimes cheaper to ship partially completed laptops to factories in Puerto Rico, Mexico, and Panama and have them c
> A national catalog and Internet retailer has three warehouses and three major distribution centers located around the country. Normally, items are shipped directly from the warehouses to the distribution centers; however, each of the distribution centers
> A computer manufacturer plans to enter new markets in three African countries—Senegal, Ghana, and Ethiopia. The company has two manufacturing facilities in China and Vietnam that can be used to supply to the new markets. Because of logi
> A sports apparel company has received an order for a college basketball team’s national championship T-shirt. The company can purchase the T-shirts from textile factories in Mexico, Puerto Rico, and Haiti. The shirts are shipped from th
> World Foods, Inc., imports food products such as meats, cheese, and pastries to the United States from warehouses at ports in Hamburg, Marseilles, and Liverpool. Ships from these ports deliver the products to Norfolk, New York, and Savannah, where they a
> Consider the following transportation problem: Formulate this problem as a linear programming model, and solve it using the computer.
> Four students Ahmed, Bob, Chandni, and David answered a survey about their preferred mobiles. Ten mobiles were demonstrated, and students were asked to rank the mobiles from 1 to 10, 10 being their highest preference. Determine two phones each student ge
> 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, fro
> The National Western Railroad’s rail network covers most of the U.S. West and Midwest. On a daily basis it sends empty freight cars from various locations in its rail network to its customers for their use. Sometimes there are not enoug
> Binford Tools manufactures garden tools. It uses inventory, overtime, and subcontracting to absorb demand fluctuations. Expected demand, regular and overtime production capacity, and subcontracting capacity are provided in the following table for the nex
> Orient Express is a global distribution company that transports its clients’ products to customers in Hong Kong, Singapore, and Taipei. All the products Orient Express ships are stored at three distribution centers—one
> Mohammed owns two trucks and accepts shipments from Dubai and transports them to Abu Dhabi. His trucks can hold up to certain load and have certain space. The following table pro- vides the capacity limits of the trucks. He has received orders from the l
> PM Computer Services produces personal computers from component parts it buys on the open market. The company can produce a maximum of 300 personal computers per month. PM wants to determine its production schedule for the first 6 months of the new year.
> Suntrek in Problem 22 supplies its finished denim jeans to its customers’ distribution centers in the United States in New York and New Orleans, and in Europe in Bristol and Marseilles. Denim jeans require 1.5 yards of denim fabric. Fol
> Suntrek in Problem 21 manufactures denim fabric at its factories in Shanghai, Karachi, and Saigon and ships it to its denim jeans manufacturing facilities in China, India, Japan, Turkey, and Italy. A bale of cotton will produce approximately 325 yards of
> Suntrek in Problem 20 ships the cotton it has purchased from the U.S. ports to overseas ports in Shanghai, Karachi, and Saigon, where its denim fabric factories are also located. The shipping and handling costs per bale of cotton from each U.S. port to e
> Suntrek, based in China, is a global supplier of denim jeans for apparel companies around the world. They purchase raw cotton from producers in Arkansas, Mississippi, and Texas, where it is picked, ginned, and baled and then transported by f latbed truck
> Solve the following linear programming problem: minimize Z = 3x11 + 12x12 + 8x13 + 10x21 + 5x22 + 6x23 + 6x31 + 7x32 + 10x33 subject to
> 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-cours
> During U.S. military action in the Middle East, large amounts of military matériel and supplies had to be shipped daily from supply depots in the United States. The critical factor in the movement of these supplies was speed. The following t
> A private taxi company in the UAE has recently procured 300 taxicabs to meet the rising demands in three cities—Dubai, Abu Dhabi, and Sharjah. Of these taxicabs, 100 are 4-seaters, 100 are 7-seaters, and 100 are 14-seater minivans. The
> Johnson Dairy procures milk from several areas, mainly from milk producers in villages, processes milk at their facilities and sells milk in packets in different cities with different prices. Since differential pricing is adopted, the profit per liter of
