Question: The Midland Tool Shop has four heavy

> Great Northwoods Outfitters is a retail phone-catalog company that specializes in outdoor clothing and equipment. A phone station at the company will be staffed with either full-time operators or temporary operators 8 hours per day. Full-time operators,

> Venture Systems is a consulting firm that develops e-commerce systems and Web sites for its clients. It has six available consultants and eight client projects under contract. The consultants have different technical abilities and experience, and as a re

> Mazy’s Department Store has decided to stay open on a 24-hour basis. The store manager has divided the 24-hour day into six 4-hour periods and determined the following minimum personnel requirements for each period: Personnel must repor

> The White Horse Apple Products Company purchases apples from local growers and makes applesauce and apple juice. It costs $0.60 to produce a jar of applesauce and $0.85 to produce a bottle of apple juice. The company has a policy that at least 30% but no

> Ahmed owns camels and sells camel milk in cans. A can will hold 3 liters of milk. To market his products, he brands his products as High-Vitamin and Low-Fat. Camel milk is processed with liquid-based vitamins, and fats and are packed in his farm. From hi

> 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 segment

> 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 s

> When Molly Lai purchased the Clean Clothes Corner Laundry, she thought that because it was in a good location near several high-income neighborhoods, she would automatically generate good business if she improved the laun- dry’s physical appearance. Thus

> 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 Problem 49, the optimal solution results in a fractional (i.e., noninteger) 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 differ

> For the transportation example in this chapter, suppose that televisions 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

> 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 fo

> 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

> Carillon Health Systems owns three hospitals, and it wants to determine which, if any, of the hospitals are inefficient. The hospital inputs each month are (1) hospital beds (100s), (2) non- physician labor (1,000s hrs.), and (3) dollar value of supplies

> Tidewater City Bank has four branches with the following inputs and outputs: The monthly output and input values for each bank are as follows: Using data envelopment analysis (DEA), determine which banks, if any, are inefficient.

> 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,

> 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 p

> 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 (ci) and selling price (pi) for each of the given months (i) are as foll

> A pottery company produces three types of products from clay: dining ware, sanitary ware, and floor tiles. The company has a stock of 500 kg of clay. A dining ware needs 2 kg of clay, sanitary ware, 4 kg, and tiles, 1 kg. The oven has space for 200 items

> 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 bon

> The Cash and Carry Building Supply Company has received the following order for boards in three lengths: The company has 25-foot standard-length boards in stock. Therefore, the standard-length boards must be cut into the lengths necessary to meet order r

> A maintenance section of a leading property company installs appliances for free in its residential and commercial properties. Whoever rents the properties can avail the free service only once at the time of moving in. After installation and during the r

> 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 sh

> 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 retain

> Suzuki Motors is a leading car manufacturer in India manufacturing cars at its Gurgaon facility. Suzuki Motors has manufactured 500 cars. These cars are to be transported to its customers in Vizag and Chennai. Four hundred cars are ordered from Chennai

> 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

> 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: (No

> 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

> 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

> 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.

> 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 m

> A confectionary store is producing two types of candies: Bulk chocolate and Mini sticks candies. Both of these candies use chocolate liquor, butter, and sugar. Currently the store has 25 lb of chocolate liquor, 16 lb of butter, and 80 lb of sugar. Candie

> 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,

> 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 do

> 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 s

> 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

> An apparel company wants to popularize its products by contacting its prospective customers. The company sets a target of contacting at least 500 men, 400 women, 300 children, and 420 schools. The company incurs £1.5 to make a daytime call a

> A furniture company produces tables, chairs, and sofas. The company uses lumber, fabric, and glass to produce these products. Labor performs the cutting, sanding, and assembly operations. The following table provides the resouce requirents of products. T

> The honorary business fraternity at Tech is planning an all-day bake sale on Saturday of a home football game as a charity fund-raising project. The members will bake cakes, cup- cakes, and cookies in one member’s apartment oven starting at 5 p.M. on Fri

> Alexis is in the first year of her undergraduate program. Her father has contributed £25,000 toward her education. From this amount she must pay her tuition for the first three years and she expects a tuition waiver for the fourth year. Since she wants t

> Gobblecakes is a bakery that specializes in cupcakes. The annual fixed cost to make cupcakes is $18,000. The variable cost including ingredients and labor to make a cupcake is $0.90. The bakery sells cupcakes for $3.20 apiece. a. If the bakery sells 12,0

> David wants to be an entrepreneur after his graduation. He is interested in toy manufacturing. After conducting market research, he estimates that his initial investment to buy brand-new toy production equipment will be $30,000; whereas for each toy, he

> 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

> 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 head of the Department of Business Analytics at Tech is determining faculty teaching schedules for the department’s 10 faculty members for next semester. There are 20 course sections scheduled over six 75-minute class periods on Tue

> 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 districts—north, south, east, west, and central—each with different hi

> 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 reform

> 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

> A fast food restaurant in Dubai needs white and dark meat to produce patties and burgers. Cost of a kg of white meat is AED10 and dark meat is AED7. Patties must contain exactly 60% white meat and 40% dark meat. A burger should contain at least 30% white

> 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 an

> 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 mone

> The Willow Furniture Company produces tables. The fixed monthly cost of production is $8,000, and the variable cost per table is $65. The tables sell for $180 apiece. a. For a monthly volume of 300 tables, determine the total cost, total revenue, and pro

> 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 b

> 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

> A greenhouse farmer plans to grow three crops—cucumber, potato, and tomato—in the forth- coming season in his farm, which spans 60 hectares. Each crop requires nitrogen, phosphoros, potassium, and micronutrients. The r

> 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.

> 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 accord- ing to the following specifications: at least 21% of metal A, no more than 1

> 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 p

> A fitter produces two types of fitting products—product A and product B—using a cutting machine (cutter) and a grinding machine (grinder). Product A requires 4 hours of the cutter and 8 hours of the grinder; product B requires 6 hours of the cutter and 4

> Solve Problem 7 using the computer.

> A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product requires two resources are as follows: a. Formulate a linear programming model to determine the optimal product mix that will maximize profit. b

> Solve the linear programming model in Problem 59 using the computer. a. Which resources constrain how many jobs Guanming can contract for? b. Guanming wants for increase either his working hours per week by 10 hours or increase the budget by HKD100. Whic

> A bakery specializes in cupcakes and chocolate cookies. The bakery estimates that cupcakes will account for 75% of its total sales, whereas chocolate cookies will account for 25% of its total sales. The annual fixed cost to make these products is $20,000

> Formulate homework Problem 38 in Chapter 1 as a linear programming model, and solve using the computer.

> Guanming wants to paint houses and commercial buildings during his summer vacation. He has two types of customers—residential and commercial. The profit from a residential property is HKD500 and from a commercial property, HKD750. A residential property

> Solve the linear programming model formulation in Problem 57 using computer. a. Are there any extra (slack) resources available? b. If the manufacturer could obtain additional resources, which one would be of most value to them? How much would they be wi

> A manufacturer produces stationeries—binder clips, pencils, erasers, and sharpeners—and packs them in boxes. A box of binder clips will have 12 pieces of binding clips; a pencil box, 12 pencils; sharpener box, 20 piece

> Solve the linear programming model formulated in Problem 55 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 m

> 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 pur

> Given the following linear programming model: transform the model into standard form and solve by using the computer.

> Solve the linear programming model formulated in Problem 52 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 sho

> 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;

> a. In Problem 50, if the pottery company determines that the profit from dining ware was £15 instead of £10, how does that affect the optimal solution? b. If the pottery company could secure additional resources, either clay or oven capacity or wheel tim

> Whitney Eggleston has quit her job in retail sales and has moved back into her parent’s house with the idea of starting an online home decor business. She plans to purchase items like decorative pillows, lamps, bowls, mirrors, etc., at craft fairs, home

> The following model was solved graphically in Chapter 2 (Problem 18): maximize Z = 5x1 + 8x2 (+, profit) subject to 3x1 + 5x2 … 50 (units, resource 1) 2x1 + 4x2 … 40 (units, resource 2) x1 … 8 (

> Solve the linear programming model formulated in Problem 48 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

> 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 t

> Solve the linear programming model formulated in Problem 46 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 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 $

> a. If Food Max in Problem 44 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 p

> 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 p

> a. In Problem 42, the capacity of the college is 3,000 students. If the university plans to increase the capacity of the college to 3,500, should the college accept this expansion? Explain. b. Analyze the number of students admitted when the capacity is

> The college of business of a large university offers six major programs and set the tuition as tabulated. The college plans to admit a total of 3,000 students in all the six majors with at least 200 students in each major. Each major should admit no more

> Solve the linear programming model formulated in Problem 39 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

> Ahmed wants to earn some extra pocket money while on his summer break, which is 5 weeks long. He plans to work for three days a week and enjoy his vacation the rest of the week. He has identified that car cleaning is a good business in his locality. He b

> Solve the linear programming model formulation in Problem 39 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 budge

> Solve the following model from Chapter 2 (Problem 9) using Excel: maximize Z = 3x1 + 6x2 (+, profit) subject to 3x1 + 2x2 … 18 (units, resource 1) x1 + x2 Ú 5 (units, resource 2) x1 … 4 (units, resource 3) x1, x2 Ú 0

> 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 Carol

> 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 sen

> 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

> Transform the following linear programming model into standard form and solve by using the computer:

> Angie Xu has converted her garage into a greenhouse with long tables where she plans to grow flower plants from seeds to sell in the spring at the downtown market. She will plant two types of flowers from seeds—daisies and impatiens. A tray of impatiens

> Use the computer to solve Problem 56 from Chapter 2 to determine how many slices of pizza and hot dogs the fraternity must sell to break even on their project to open a food booth at the football stadium.

> Solve the linear programming model formulated in Problem 31 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 he

> Solve the linear programming model formulated in Problem 31 for Alexis Harrington graphically. a. How much would the return for cattle have to increase for Alexis to invest only in cattle? b. Should all of Alexis’s inheritance be invested according to th

> Kathleen Taylor is a high school student who has been investigating the possibility of mowing lawns for a summer job. She has a couple of friends she thinks she could hire on an hourly basis per job. The equipment, including two new lawnmowers and weed-e

> 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 inv

> Solve the linear programming model formulated in Problem 29 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 so

> Given the following Excel spreadsheet for a linear programming model and Solver Parameters window, indicate the formula for cell B13 and fill in the Solver Parameters window with the appropriate information to solve the problem:

> 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.