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Questions and Answers of Finance

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
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
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
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
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 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
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.
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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,
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
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
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
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
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
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
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.
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
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
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
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
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
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
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.

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