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

Andy Mendoza in Problem 7 is concerned that the demand for his dolls will not exceed the break-even point. He believes he can reduce his initial investment by purchasing used sewing machines and fewer machines. This will reduce his initial investment from $25,000 to $17,000.However, it will also
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 store has noticed that several pizza delivery
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 “executive” plan charges a fixed fee of $100
Annie Russell, a student at Tech, plans to open a hot dog stand inside Tech’s football stadium during home games. There are seven home games scheduled for the upcoming season. She must pay the Tech athletic department a vendor’s fee of $3,000 for the season. Her stand and other equipment will
Hannah Byers and Kathleen Taylor are considering the possibility of teaching swimming to kids during the summer. A local swim club opens its pool at noon each day, so it is available to rent during the morning. The cost of renting the pool during the 10-week period for which Hannah and Kathleen
The College of Business at Tech is planning to begin an online MBA program. The initial startup cost for computing equipment, facilities, course development, and staff recruitment and development is $350,000. The college plans to charge tuition of $18,000 per student per year. However, the
The Star Youth Soccer Club helps to support its 20 boys’ and girls’ teams financially, primarily through the payment of coaches. The club puts on a tournament each fall to help pay its expenses. The cost of putting on the tournament is $8,000, mainly for development, printing, and mailing of
A group of developers is opening a health club near a new housing development. The health club—which will have exercise and workout equipment, basketball courts, swimming pools, an indoor walking/running track, and tennis courts—is one of the amenities the developers are building to attract new
The Tech Student Government Association (SGA) has several campus projects it undertakes each year and its primary source of funding to support these projects is a T-shirt sale in the fall for what is known as the “orange effect” football game (with orange being one of Tech’s colors). The
The owners of Backstreets Italian Restaurant are considering starting a delivery service for pizza and their other Italian dishes in the small college town where they are located. They can purchase a used delivery van and have it painted with their name and logo for $21,500.They can hire part-time
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-eaters, would cost her $500, and she estimates
The Weemow Lawn Service mows its customers’ lawns and provides lawn maintenance starting in the spring, through the summer, and into the early fall. During the winter, the service doesn’t operate, and Weemow’s owners, Jeff and Julie Weems, find part-time jobs. They are considering the
In the example used to demonstrate model construction in this chapter (p. 4), 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 constructed ismaximize Z = 20x - 5xsubject
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 produce a unit of y. The profit for x is $30
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 make bowls and mugs, and it takes her 12 hours
The Easy Drive Car Rental Agency needs 500 new cars in its Nashville operation and 300 new cars in Jacksonville, and it currently has 400 new cars in both Atlanta and Birmingham. It costs $30 to move a car from Atlanta to Nashville, $70 to move a car from Atlanta to Jacksonville, $40 to move a car
When Tracy McCoy wakes up on Saturday morning, she remembers that she promised the PTA she would make some cakes and/or homemade bread for its bake sale that afternoon. However, she does not have time to go to the store and get ingredients, and she has only a short time to bake things in her oven.
The local Food King grocery store has eight possible checkout stations with registers. On Saturday mornings customer traffic is relatively steady from 8 A.M. to noon. The store manager would like to determine how many checkout stations to staff during this time period. The manager knows from
A furniture manufacturer in Roanoke, Virginia, must deliver a tractor trailer load of furniture to a retail store in Washington, DC. There are a number of different routes the truck can take from Roanoke to DC, as shown in the following road network, with the distance for each segment shown in
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 laundry’s physical appearance. Thus, she initially invested a lot of her cash
Vicki Smith, Penny Miller, and Darryl Davis are students at State University. In the summer they often go rafting with other students down the Ocobee River in the nearby Blue Ridge Mountain foothills. The river has a number of minor rapids but is not generally dangerous. The students' rafts
The town of Draper, with a population of 20,000, sits adjacent to State University, which has an enrollment of 27,000 students. Downtown Draper merchants have long complained about the lack of parking available to their customers. This is one primary reason for the steady migration of downtown
In Problem 34 in Chapter 1, when Tracy McCoy wakes up Saturday morning, she remembers that she promised the PTA she would make some cakes and/or homemade bread for its bake sale that afternoon. However, she does not have time to go to the store to get ingredients, and she has only a short time to
A company produces two products that are processed on two assembly lines. Assembly line 1 has 100 available hours, and assembly line 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 product 1 requires 7 hours and product 2 requires 3 hours. The
The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin A and
The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phosphate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phosphate, and 1 ounce
The Pinewood Furniture Company produces chairs and tables from two resources—labor and wood. The company has 80 hours of labor and 36 board-ft. of wood available each day. Demand for chairs is limited to 6 per day. Each chair requires 8 hours of labor and 2 board-ft. of wood, whereas a table
In Problem 6, how much labor and wood will be unused if the optimal numbers of chairs and tables are produced?
In Problem 6, explain the effect on the optimal solution of changing the profit on a table from $100 to $500.
The Crumb and Custard Bakery makes coffee cakes and Danish pastries in large pans. The main ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available, and the demand for coffee cakes is 5. Five pounds of flour and 2 pounds of sugar are required to make a pan of
In Problem 9, how much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked?
Solve the following linear programming model graphically:Maximize Z = 3x1 + 6x2subject to3x1 + 2x2 ≤ 18x1 + x2 ≥ 5x1 ≤ 4x1, x2 ≥ 0
The Elixer Drug Company produces a drug from two ingredients. Each ingredient contains the same three antibiotics, in different proportions. One gram of ingredient 1 contributes 3 units, and 1 gram of ingredient 2 contributes 1 unit of antibiotic 1; the drug requires 6 units. At least 4 units of
A jewelry store makes necklaces and bracelets from gold and platinum. The store has 18 ounces of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2 ounces of platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of platinum. The demand for bracelets is no
In Problem 13, explain the effect on the optimal solution of increasing the profit on a bracelet from $400 to $600. What will be the effect of changing the platinum requirement for a necklace from 2 ounces to 3 ounces?
In Problem 13:a. The maximum demand for bracelets is four. If the store produces the optimal number of bracelets and necklaces, will the maximum demand for bracelets be met? If not, by how much will it be missed?b. What profit for a necklace would result in no bracelets being produced, and what
A clothier makes coats and slacks. The two resources required are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square yards of wool and 4
In Problem 16, what would be the effect on the optimal solution if the available labor were increased from 200 to 240 hours?
The Weemow Lawn Service wants to start doing snow removal in the winter when there are no lawns to maintain. Jeff and Julie Weems, who own the service, are trying to determine how much equipment they need to purchase, based on the various job types they have. They plan to work themselves and hire
In Problem 18:a. If Jeff and Julie pay $3,700 for snow removal equipment, will they make any money?b. If Jeff and Julie reduce their prices to $30 for a driveway and $100 for a parking lot, they will increase demand to 55 for driveways and 32 for businesses. Will this affect their possible
Solve the following linear programming model graphically:maximize Z = 1.5x1 + x2subject tox1 ≤ 4x2 ≤ 6x1 + x2 ≤ 5x1, x2 ≥ 0
Transform the model in Problem 20 into standard form and indicate the value of the slack variables at each corner point solution.
Solve the following linear programming model graphically:maximize Z = 5x1 + 8x2subject to3x1 + 5x2 ≤ 502x1 + 4x2 ≤ 40x1 ≤ 8x2 ≤ 10x1, x2 ≥ 0
Transform the model in Problem 22 into standard form and indicate the value of the slack variables at each corner point solution.
Solve the following linear programming model graphically:maximize Z = 6.5x1 + 10x2subject to2x1 + 4x2 ≤ 40x1 + x2 ≤ 15x1 ≥ 8x1, x2 ≥ 0
Universal Claims Processors processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary
In Problem 26, explain the effect on the optimal solution of changing the daily pay for a permanent claims processor from $64 to $54. Explain the effect of changing the daily pay for a temporary claims processor from $42 to $36.
Solve the following linear programming model graphically:minimize Z = 8x1 + 6x2subject to4x1 + 2x2 ≥ 20-6x1 + 4x2 ≤ 12x1 + x2 ≥ 6x1, x2 ≥ 0
Solve the following linear programming model graphically:minimize Z = 3x1 + 6x2subject to3x1 + 2x2 ≤ 18x1 + x2 ≥ 5x1 ≤ 4x2 ≤ 7x2/x1 ≤ 7/8x1, x2 ≥ 0
Solve the following linear programming model graphically:minimize Z = 5x1 + x2subject to3x1 + 4x2 = 24x1 ≤ 6x1 + 3x2 ≤ 12x1, x2 ≥ 0
Solve the following linear programming model graphically:maximize Z = 3x1 + 2x2subject to2x1 + 4x2 ≤ 22-x1 + 4x2 ≤ 104x1 - 2x2 ≤ 14x1 - 3x2 ≤ 1x1, x2 ≥ 0
Solve the following linear programming model graphically:minimize Z = 8x1 + 2x2subject to2x1 - 6x2 ≤ 125x1 + 4x2 ≥ 40x1 + 2x2 ≥ 12x2 ≤ 6 x1, x2 ≥ 0
Gillian’s Restaurant has an ice-cream counter where it sells two main products, ice cream and frozen yogurt, each in a variety of flavors. The restaurant makes one order for ice cream and yogurt each week, and the store has enough freezer space for 115 gallons total of both products. A gallon of
Copperfield Mining Company owns two mines, each of which produces three grades of ore—high, medium, and low. The company has a contract to supply a smelting company with at least 12 tons of high-grade ore, 8 tons of medium-grade ore, and 24 tons of low-grade ore. Each mine produces a certain
A canning company produces two sizes of cans—regular and large. The cans are produced in 10,000-can lots. The cans are processed through a stamping operation and a coating operation. The company has 30 days available for both stamping and coating. A lot of regular-size cans requires 2 days to
A manufacturing firm produces two products. Each product must undergo an assembly process and a finishing process. It is then transferred to the warehouse, which has space for only a limited number of items. The firm has 80 hours available for assembly and 112 hours for finishing, and it can store
Assume that the objective function in Problem 40 has been changed from Z = 30X1 + 70x2 to Z = 90x1 + 70x2. Determine the slope of each objective function and discuss what effect these slopes have on the optimal solution.
The Valley Wine Company produces two kinds of wine—Valley Nectar and Valley Red. The wines are produced from 64 tons of grapes the company has acquired this season. A 1,000-gallon batch of Nectar requires 4 tons of grapes, and a batch of Red requires 8 tons. However, production is limited by the
In Problem 42:a. How much processing time will be left unused at the optimal solution?b. What would be the effect on the optimal solution of increasing the available storage space from 50 to 60 cubic yards?
Kroeger supermarket sells its own brand of canned peas as well as several national brands. The store makes a profit of $0.28 per can for its own peas and a profit of $0.19 for any of the national brands. The store has 6 square feet of shelf space available for canned peas, and each can of peas
In Problem 44, if Kroeger discounts the price of its own brand of peas, the store will sell at least 1.5 times as much of the national brands as its own brand, but its profit margin on its own brand will be reduced to $0.23 per can. What effect will the discount have on the optimal solution?
Shirtstop makes T-shirts with logos and sells them in its chain of retail stores. It contracts with two different plants—one in Puerto Rico and one in The Bahamas. The shirts from the plant in Puerto Rico cost $0.46 apiece, and 9% of them are defective and can’t be sold. The shirts from The
In Problem 46:a. Suppose Shirtstop decided it wanted to minimize the defective shirts while keeping costs below $2,000. Reformulate the problem with these changes and solve graphically.b. How many fewer defective items were achieved with the model in (a) than with the model in Problem 46?
Angela and Bob Ray keep a large garden in which they grow cabbage, tomatoes, and onions to make two kinds of relish—chow-chow and tomato. The chow-chow is made primarily of cabbage, whereas the tomato relish has more tomatoes than does the chow-chow. Both relishes include onions, and negligible
In Problem 48, the Rays have checked their sales records for the past 5 years and have found that they sell at least 50% more chow-chow than tomato relish. How will this additional information affect their model and solution?
A California grower has a 50-acre farm on which to plant strawberries and tomatoes. The grower has available 300 hours of labor per week and 800 tons of fertilizer, and he has contracted for shipping space for a maximum of 26 acres’ worth of strawberries and 37 acres’ worth of tomatoes. An acre
In Problem 50, if the amount of fertilizer required for each acre of strawberries were determined to be 20 tons instead of 8 tons, what would be the effect on the optimal solution?
The admissions office at Tech wants to determine how many in-state and how many out-of-state students to accept for next fall’s entering freshman class. Tuition for an in-state student is $7,600 per year, whereas out-of-state tuition is $22,500 per year. A total of 12,800 in-state and 8,100
The Robinsons are planning a wedding and reception for their daughter, Rachel. Some of the most expensive items served at the reception and dinner are wine and beer. The Robinsons are planning on 200 guests at the reception, and they estimate that they need at least four servings (i.e., a glass of
Suppose that in Problem 53, it turns out that twice as many guests prefer wine as beer. Will the Robinsons have enough wine with the amount they ordered in the Problem 53 solution? How much waste will there be with the solution in Problem 53?
Xara Stores in the United States imports the designer-inspired clothes it sells from suppliers in China and Brazil. Xara estimates that it will have 45 orders in a year, and it must arrange to transport orders (in less-than-full containers) by container ship with shippers in Hong Kong and Buenos
In Problem 55, the Chinese shipper would like to gain more shipping orders from Xara because it’s a prestigious company and would enhance the shipper’s reputation. It has therefore made the following proposals to Xara:a. Would Xara give the Chinese shipper more orders if it reduced its shipping
Janet Lopez is establishing an investment portfolio that will include stock and bond funds. She has $720,000 to invest, and she does not want the portfolio to include more than 65% stocks. The average annual return for the stock fund she plans to invest in is 18%, whereas the average annual return
Professor Smith teaches two sections of business statistics, which combined will result in 120 final exams to be graded. Professor Smith has two graduate assistants, Brad and Sarah, who will grade the final exams. There is a 3-day period between the time the exam is administered and when final
In Problem 58, if Professor Smith could hire Brad or Sarah to work 1 additional hour, which should she choose? What would be the effect of hiring the selected graduate assistant for 1 additional hour?
Starbright Coffee Shop at the Galleria Mall serves two coffee blends it brews on a daily basis, Pomona and Coastal. Each is a blend of three high-quality coffees from Colombia, Kenya, and Indonesia. The coffee shop has 6 pounds of each of these coffees available each day. Each pound of coffee will
In Problem 60:a. If Starbright Coffee Shop could get 1 more pound of coffee, which one should it be? What would be the effect on sales of getting 1 more pound of this coffee? Would it benefit the shop to increase its brewing capacity from 30 gallons to 40 gallons?b. If the shop spent $20 per day on
Solve the following linear programming model graphically and explain the solution result:minimize Z = +3,000x1 + 1,000x2subject to60x1 + 20x2 ≥ 1,20010x1 + 10x2 ≥ 40040x1 + 160x2 ≥ 2,400x1, x2 ≥ 0
Solve the following linear programming model graphically and explain the solution result:maximize Z = 60x1 + 90x2subject to60x1 + 30x2 ≤ 1,500100x1 + 100x2 ≥ 6,000x2 ≥ 30x1, x2 ≥ 0
Solve the following linear programming model graphically and explain the solution result:maximize Z = 110x1 + 75x2subject to2x1 + x2 ≥ 40-6x1 + 8x2 ≤ 12070x1 + 105x2 ≥ 2,100x1, x2 ≥ 0
The Metropolitan Police Department was recently criticized in the local media for not responding to police calls in the downtown area rapidly enough. In several recent cases, alarms had sounded for break-ins, but by the time the police car arrived, the perpetrators had left, and in one instance a
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. There were no other French restaurants in
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 from college. As a result, she has $120,000
Given the following QM for Windows computer solution of a linear programming model, graph the problem and identify the solution point, including variable values and slack, from the computeroutput:
Given the following Excel spreadsheet for a linear programming model and Solver Parameters window, indicate the formula for cell B13 and fill in the Solver Parameters window with the appropriate information to solve theproblem:
The following model was solved graphically in Chapter 2 (Problem 22):maximize Z = 5x1 + 8x2 ($, profit)subject to3x1 + 5x2 ‰¤ 50 (units, resource 1)2x1 + 4x2 ‰¤ 40 (units, resource 2)x1 ‰¤ 8 (units, resource 3)x2 ‰¤ 10 (units, resource 4)x1 , x2
Given the following graph of a linear programming model with a single constraint and the objective function maximize Z = 30x1 + 50x2 , determine the optimal solution point:Determine the values by which c1 and c2 must decrease or increase in order to change the current solution point to the other
Southern Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources€”rubber and leather. The resource requirements for each product and the total resources available are as follows:Each basketball produced results in a profit of $12, and each
Solve the model formulated in Problem 7 for Southern Sporting Goods Company graphically.a. Identify the amount of unused resources (i.e., slack) at each of the graphical extreme points.b. What would be the effect on the optimal solution if the profit for a basketball changed from $12 to $13? What
For the linear programming model for Southern Sporting Goods Company, formulated inProblem 7 and solved graphically in Problem 8:a. Determine the sensitivity ranges for the objective function coefficients and constraint quantity values, using graphical analysis.b. Verify the sensitivity ranges
A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows:a. Formulate a linear programming model to determine the optimal product mix that will maximize
Solve Problem 10 graphically.a. Identify the amount of unused resources (i.e., slack) at each of the graphical extreme points.b. What would be the effect on the optimal solution if the production time on line 1 was reduced to 40 hours?c. What would be the effect on the optimal solution if the
For the linear programming model formulated in Problem 10 and solved graphically in Problem 11:a. Determine the sensitivity ranges for the objective function coefficients, using graphical analysis.b. Verify the sensitivity ranges determined in (a) by using the computer.c. Using the computer,
Irwin Textile Mills produces two types of cotton cloth—denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time; a yard
Solve the model formulated in Problem 13 for Irwin Textile Mills graphically.a. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met?b. What is the effect on the optimal solution if the profit per yard of denim is increased from $2.25 to
Solve the linear programming model formulated in Problem 13 for Irwin Mills by using the computer.a. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer.b. Identify the sensitivity ranges for the objective function
United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a different production capacity (in tons per day) for each grade, as follows:The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade
Solve the linear programming model formulated in Problem 16 for United Aluminum Company graphically.a. How much extra (i.e., surplus) high-, medium-, and low-grade aluminum does the company produce at the optimal solution?b. What would be the effect on the optimal solution if the cost of operating
Solve the linear programming model formulated in Problem 16 for United Aluminum Company by using the computer.a. Identify and explain the shadow prices for each of the aluminum grade contract requirements.b. Identify the sensitivity ranges for the objective function coefficients and the constraint
The Bradley family owns 410 acres of farmland in North Carolina on which they grow corn and tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest; each acre of tobacco costs $210. The Bradleys have a budget of $52,500 for next year. The government limits the number of acres of

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