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 every- one eats a lot of food. She has to pay $1,000 per game for a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. She thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans, and so these are the items she would sell. Most food items are sold during the hour before the game starts and during halftime; thus it will not be possible for Julia to prepare the food while she is selling it. She must prepare the food ahead of time and then store it in a warming oven. For $600 she can lease a warming oven for the six- game home season. The oven has 16 shelves, and each shelf is 3 feet by 4 feet. She plans to fill the oven with the three food items before the game and then again before halftime. Julia has negotiated with a local pizza delivery company to deliver 14-inch cheese pizzas twice each game—2 hours before the game and right after the opening kickoff. Each pizza will cost her $6 and will include 8 slices. She esti- mates it will cost her $0.45 for each hot dog and $0.90 for each barbecue sandwich if she makes the barbecue herself the night before. She measured a hot dog and found it takes up about 16 square inches of space, whereas a barbecue sandwich takes up about 25 square inches. She plans to sell a slice of pizza and a hot dog for $1.50 apiece and a barbecue sandwich for $2.25. She has $1,500 in cash available to purchase and prepare the food items for the first home game; for the remaining five games she will purchase her ingredients with money she has made from the previous game. Julia has talked to some students and vendors who have sold food at previous football games at Tech as well as at other universities. From this she has discovered that she can expect to sell at least as many slices of pizza as hot dogs and barbecue sandwiches combined. She also anticipates that she will probably sell at least twice as many hot dogs as bar- becue sandwiches. She believes that she will sell everything she can stock and develop a customer base for the season if she follows these general guidelines for demand. If Julia clears at least $1,000 in profit for each game after paying all her expenses, she believes it will be worth leasing the booth. A. Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth. B. If Julia were to borrow some more money from a friend before the first game to purchase more ingredients, could she increase her profit? If so, how much should she borrow, and how much additional profit would she make? What factor constrains her from bor- rowing even more money than this amount (indicated in your answer to the previous question)? C. When Julia looked at the solution in (A), she realized that it would be physically difficult for her to prepare all the hot dogs and barbecue sandwiches indicated in this solution. She believes she can hire a friend of hers to help her for $100 per game. Based on the results in (A) and (B), is this something you think she could reasonably do and should do? D. Julia seems to be basing her analysis on the assump- tion that everything will go as she plans. What are some of the uncertain factors in the model that could go wrong and adversely affect Julia’s analysis? Given these uncertainties and the results in (A), (B), and (C), what do you recommend that Julia do?
> 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
> 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
> 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
> 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
> In Problem 15, the school board determined that it does not want any of the schools to be overly crowded compared with the other schools. It would like to assign students from each district to each school so that enrollments are evenly balanced between t
> Bayville has built a new elementary school, increasing the town’s total to four schools— Addison, Beeks, Canfield, and Daley. Each has a capacity of 400 students. The school board wants to assign children to schools so
> A national grain trader procures wheat in standard bags of 50 kg from several farmers and sends the wheat bags to different retail outlets. The supply from the different farmers are given in the following table: The demand of each retail outletsis: Wheat
> A large manufacturing company is closing three of its existing plants and intends to transfer some of its more skilled employees to three plants that will remain open. The number of employees available for transfer from each closing plant is as follows:
> A severe winter ice storm has swept across North Carolina and Virginia, followed by over a foot of snow and frigid, single-digit temperatures. These weather conditions have resulted in numerous downed power lines and power outages, causing dangerous cond
> IP-computers assembles computers in three countries (the US, China, and Malaysia). The production capacities of the three assembly plants are: The company exports the computers to three other countries (Korea, Iran, and Ukraine). The demand at the differ
> Essex Energy Company has a contract to deliver 400 tons of coal to China. The company has mines in the following regions—Appalachia (WV, KY, and VA), Mississippi (IL and IN), and Midwest (MO, IA, and NE)—and it ships c
> 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 colleg
> David from Problem 16 is now concerned as the market demand does not look very promising, and he may not be able to sell more than the breakeven volume. Therefore, instead of buying brand- new equipment, he plans on buying used equipment for $20,000 to r
> A transportation problem involves the following costs, supply, and demand: Solve this problem by using the computer.
> Helen Holmes makes pottery by hand in her basement. She has 20 hours available each week to make bowls and vases. A bowl requires 3 hours of labor, and a vase requires 2 hours of labor. It requires 2 pounds of special clay to make a bowl and 5 pounds to
> Samsung sells its four flagship products—cell phones, TVs, computing devices, and memory storage devices—through its exclusive showroom in a city. To support sales, it has hired 20 per- sons and trained them to service every product. Depending on the nat
> A glassblower makes glass decanters and glass trays on a weekly basis. Each item requires 1 pound of glass, and the glassblower has 15 pounds of glass available each week. A glass decanter requires 4 hours of labor, a glass tray requires only 1 hour of l
> A jeweler and her apprentice make silver pins and necklaces by hand. Each week they have 80 hours of labor and 36 ounces of silver available. It requires 8 hours of labor and 2 ounces of silver to make a pin and 10 hours of labor and 6 ounces of silver t
> A tailor makes wool tweed sport coats and wool slacks. He is able to get a shipment of 150 square yards of wool cloth from Scotland each month to make coats and slacks, and he has 200 hours of his own labor to make them each month. A coat requires 3 squa
> A business undergraduate student must register for the next semester on or before the drop date. The student meets instructors and assesses potential grades and study-hour requirements. There are eight courses offered in his major. The following table sh
> A state government plans to set up new police stations for the public. The state has seven districts (A through G). Each police station can serve a radius of 30 miles. A district may receive service from more than one police station. The following tables
> The BigRig Trucking Company participates in an Internet transportation exchange where customers advertise their shipments including load weight and volume, and trip origin and destination. BigRig then computes the cost and time of the trip and determines
> The Valley Times and World News publish and deliver a morning newspaper 7 days a week. The bundled papers are delivered by trucks to a number of area communities where they are picked up by carriers at a central location in the community, who then delive
> Annabelle Sizemore has cashed in some treasury bonds and a life insurance policy that her parents had accumulated over the years for her. She has also saved some money in certificates of deposit and savings bonds during the 10 years since she graduated f
> HTM Realty has a storefront rental property in downtown Draperton, a small college town next to the Tech campus. The property encompasses four business spaces that open onto College Avenue. HTM has a long-term tenant in each space, and their leases are a
> A car manufacturer produces cars in five colors: Red, Green, Blue, White, and Yellow. Only one painting machine is available now for painting cars. The machine must be stopped if the machine is required to use a different color. The time between this cha
> The Tech Software School contracts to train employees of companies in the use of various soft- ware products and packages. The training programs are all delivered on three consecutive days but require different daily durations, depending on the software
> An investment firm received R120,000 from a client for investment. The firm has identified six options and their expected returns are as given in the following table. Each option needs a mini- mum entry amount for that investment as given in the cost col
> The Kreeger Grocery Store chain has bought out a competing grocery store chain. However, it now has too many stores in close proximity to each other in certain cities. In Roanoke the chain has 10 stores, and it does not want any stores closer than 2 mile
> An oil refinery pumps thousands of barrels of crude and refines it to produce fuels. The refinery must plan its production for the next four months to meet its expected demand. The monthly production capacity of the oil refinery is 12 barrels. It does no
> An industrial machinery manufacturer produces shapers and drill presses. The manufacturer fore- casts that the demand for shapers for the next month will be at least 5 and the demand for drill presses for the next month will be at most 7. A shaper earns
> Globex Investment Capital Corporation owns six companies that have the following estimated returns (in millions of dollars) if sold in one of the next 3 years: To operating funds, the company must sell at least $20 million worth of assets in year 1, $25
> Wins above replacement,” or WAR, is a complex statistical measure of a major league baseball player’s performance that sums up a player’s total contribution to a team using various offensive and defen
> A healthcare company plans to open its new chain of clinics in seven cities (1 to 7) within its earmarked budget. The population size (in thousands) in cities and associated investment budgets are tabulated below. The company has earmarked 90 lakhs for t
> Angela Fox and Zooey Caulfield were food and nutrition majors at State University, as well as close friends and roommates. Upon graduation Angela and Zooey decided to open a French restaurant in Draperton, the small town where the university was located.
> Rowntown Cab Company has 70 drivers that it must schedule in three 8-hour shifts. However, the demand for cabs in the metropolitan area varies dramatically according to the time of day. The slowest period is between midnight and 4:00 A.M. The dispatcher
> Tech offers a number of off-campus courses in its professional and executive masters of information technology (MIT) programs at various locations around the state. The courses are taught by a group of regular Tech information technology faculty and adju
> A petroleum refinery in Dubai wants to expand its refinery and stock-yard for the expected surge in the oil prices in the coming years. The company has four distinct activities in its strategic plan—plant expansion, stockyard improvemen
> Sobha Real Estate Company constructs residential apartments in several countries. It plans to evaluate the worthiness of five potential construction sites over the next three years and choose the ones that lead to maximum return. The following table give
> A carpenter makes tables and chairs from wood and steel. His store has 200 units of wood and 200 units of steel. Each table requires 5 units of wood and 2 units of steel, whereas each chair requires 2 units of wood and 4 units of steel. The demand for th
> A truck manufacturer has three manufacturing plants and four retail outlets. The details of the demand at outlets, supply at plants, and the cost to transport between plants and outlets in lakhs (a lakh is a unit in the Indian numbering system equal to o
