Discussion Questions and Problems
Discussion Questions
1-1 What is the difference between quantitative and qualitative analysis? Give several examples.
1-2 Define quantitative analysis. What are some of the organizations that support the use of the scientific approach?
1-3 What are the three categories of business analytics?
1-4 What is the quantitative analysis process? Give several examples of this process.
1-5 Briefly trace the history of quantitative analysis. What happened to the development of quantitative analysis during World War II?
1-6 Give some examples of various types of models. What is a mathematical model? Develop two examples of mathematical models.
1-7 List some sources of input data.
1-8 What is implementation, and why is it important?
1-9 Describe the use of sensitivity analysis and postoptimality analysis in analyzing the results.
1-10 Managers are quick to claim that quantitative analysts talk to them in a jargon that does not sound like English. List four terms that might not be understood by a manager. Then explain in nontechnical language what each term means.
1-11 Why do you think many quantitative analysts don’t like to participate in the implementation process? What could be done to change this attitude?
1-12 Should people who will be using the results of a new quantitative model become involved in the technical aspects of the problem-solving procedure?
1-13 C. W. Churchman once said that “mathematics … tends to lull the unsuspecting into believing that he who thinks elaborately thinks well.” Do you think that the best QA models are the ones that are most elaborate and complex mathematically? Why?
1-14 What is the break-even point? What parameters are necessary to find it?
Note: means the problem may be solved with QM for Windows; means the problem may be solved with Excel QM; and means the problem may be solved with QM for Windows and/or Excel QM.
Problems
1-15 Gina Fox has started her own company, Foxy Shirts, which manufactures imprinted shirts for special occasions. Since she has just begun this operation, she rents the equipment from a local printing shop when necessary. The cost of using the equipment is $350. The materials used in one shirt cost $8, and Gina can sell these for $15 each.
If Gina sells 20 shirts, what will her total revenue be? What will her total variable cost be?
How many shirts must Gina sell to break even? What is the total revenue for this?
1-16 Ray Bond sells handcrafted yard decorations at county fairs. The variable cost to make these is $20 each, and he sells them for $50. The cost to rent a booth at the fair is $150. How many of these must Ray sell to break even?
1-17 Ray Bond, from Problem 1-16, is trying to find a new supplier that will reduce his variable cost of production to $15 per unit. If he was able to succeed in reducing this cost, what would the break-even point be?
1-18 Katherine D’Ann is planning to finance her college education by selling programs at the football games for State University. There is a fixed cost of $400 for printing these programs, and the variable cost is $3. There is also a $1,000 fee that is paid to the university for the right to sell these programs. If Katherine was able to sell programs for $5 each, how many would she have to sell in order to break even?
1-19 Katherine D’Ann, from Problem 1-18, has become concerned that sales may fall, as the team is on a terrible losing streak and attendance has fallen off. In fact, Katherine believes that she will sell only 500 programs for the next game. If it was possible to raise the selling price of the program and still sell 500, what would the price have to be for Katherine to break even by selling 500?
1-20 Farris Billiard Supply sells all types of billiard equipment and is considering manufacturing its own brand of pool cues. Mysti Farris, the production manager, is currently investigating the production of a standard house pool cue that should be very popular. Upon analyzing the costs, Mysti determines that the materials and labor cost for each cue is $25 and the fixed cost that must be covered is $2,400 per week. With a selling price of $40 each, how many pool cues must be sold to break even? What would the total revenue be at this break-even point?
1-21 Mysti Farris (see Problem 1-20) is considering raising the selling price of each cue to $50 instead of $40. If this is done while the costs remain the same, what would the new break-even point be? What would the total revenue be at this break-even point?
1-22 Mysti Farris (see Problem 1-20) believes that there is a high probability that 120 pool cues can be sold if the selling price is appropriately set. What selling price would cause the break-even point to be 120?
1-23 Golden Age Retirement Planners specializes in providing financial advice for people planning for a comfortable retirement. The company offers seminars on the important topic of retirement planning. For a typical seminar, the room rental at a hotel is $1,000, and the cost of advertising and other incidentals is about $10,000 per seminar. The cost of the materials and special gifts for each attendee is $60 per person attending the seminar. The company charges $250 per person to attend the seminar, as this seems to be competitive with other companies in the same business. How many people must attend each seminar for Golden Age to break even?
1-24 A couple of entrepreneurial business students at State University decided to put their education into practice by developing a tutoring company for business students. While private tutoring was offered, it was determined that group tutoring before tests in the large statistics classes would be most beneficial. The students rented a room close to campus for $300 for 3 hours. They developed handouts based on past tests, and these handouts (including color graphs) cost $5 each. The tutor was paid $25 per hour, for a total of $75 for each tutoring session.
If students are charged $20 to attend the session, how many students must enroll for the company to break even?
A somewhat smaller room is available for $200 for 3 hours. The company is considering this possibility. How would this affect the break-even point?
1-25 Zoe Garcia is the manager of a small office-support business that supplies copying, binding, and other services for local companies. Zoe must replace a worn-out copy machine that is used for black-and-white copying. Two machines are being considered, and each of these has a monthly lease cost plus a cost for each page that is copied. Machine 1 has a monthly lease cost of $600, and there is a cost of $0.010 per page copied. Machine 2 has a monthly lease cost of $400, and there is a cost of $0.015 per page copied. Customers are charged $0.05 per page for copies.
What is the break-even point for each machine?
If Zoe expects to make 10,000 copies per month, what would be the cost for each machine?
If Zoe expects to make 30,000 copies per month, what would be the cost for each machine?
At what volume (the number of copies) would the two machines have the same monthly cost? What would the total revenue be for this number of copies?
1-26 Bismarck Manufacturing intends to increase capacity through the addition of new equipment. Two vendors have presented proposals. The fixed cost for proposal A is $65,000 and for proposal B, $34,000. The variable cost for A is $10 and for B, $14. The revenue generated by each unit is $18.
What is the break-even point for each proposal?
If the expected volume is 8,300 units, which alternative should be chosen?
Case Study Food and Beverages at Southwestern University Football Games
Southwestern University (SWU), a large state college in Stephenville, Texas, 30 miles southwest of the Dallas/Fort Worth metroplex, enrolls close to 20,000 students. The school is the dominant force in the small city, with more students during fall and spring than permanent residents.
A longtime football powerhouse, SWU is a member of the Big Eleven conference and is usually in the top 20 in college football rankings. To bolster its chances of reaching the elusive and long-desired number-one ranking, in 2013 SWU hired the legendary Billy Bob Dillon as its head coach. Although the number-one ranking remained out of reach, attendance at the six Saturday home games each year increased. Prior to Dillon’s arrival, attendance generally averaged 25,000–29,000. Season ticket sales bumped up by 10,000 just with the announcement of the new coach’s arrival. Stephenville and SWU were ready to move to the big time!
With the growth in attendance came more fame, the need for a bigger stadium, and more complaints about seating, parking, long lines, and concession stand prices. Southwestern University’s president, Dr. Marty Starr, was concerned not only about the cost of expanding the existing stadium versus building a new stadium but also about the ancillary activities. He wanted to be sure that these various support activities generated revenue adequate to pay for themselves. Consequently, he wanted the parking lots, game programs, and food service to all be handled as profit centers. At a recent meeting discussing the new stadium, Starr told the stadium manager, Hank Maddux, to develop a break-even chart and related data for each of the centers. He instructed Maddux to have the food service area break-even report ready for the next meeting. After discussion with other facility managers and his subordinates, Maddux developed the following table showing the suggested selling prices, his estimate of variable costs, and his estimate of the percentage of the total revenues that would be expected for each of the items based on historical sales data.
Maddux’s fixed costs are interesting. He estimated that the prorated portion of the stadium cost would be as follows: salaries for food services at $300,000 ($60,000 for each of the six home games); 2,400 square feet of stadium space at $5 per square foot per game; and six people per booth in each of the six booths for 5 hours at $12 an hour. These fixed costs will be proportionately allocated to each of the products based on the percentages provided in the table. For example, the revenue from soft drinks would be expected to cover 25% of the total fixed costs.
| ITEM | SELLING PRICE/UNIT | VARIABLE COST/UNIT | PERCENT REVENUE |
|---|---|---|---|
| Soft drink | $5.00 | $1.50 | 25% |
| Coffee | 4.00 | 1.00 | 25 |
| Hot dogs | 6.00 | 2.00 | 20 |
| Hamburgers | 7.50 | 3.00 | 20 |
| Misc. snacks | 2.00 | 1.00 | 10 |
Maddux wants to be sure that he has a number of things for President Starr: (1) the total fixed cost that must be covered at each of the games; (2) the portion of the fixed cost allocated to each of the items; (3) what his unit sales would be at breakeven for each item—that is, what sales of soft drinks, coffee, hot dogs, hamburgers, and snacks are necessary to cover the portion of the fixed cost allocated to each of these items; (4) what the dollar sales for each of these would be at these break-even points; and (5) realistic sales estimates per attendee for attendance of 60,000 and 35,000. (In other words, he wants to know how many dollars each attendee is spending on food at his projected break-even sales at present and if attendance grows to 60,000.) He felt this last piece of information would be helpful to understand how realistic the assumptions of his model are, and this information could be compared with similar figures from previous seasons.
Discussion Question
Prepare a brief report for Dr. Starr that covers the items noted.
HEIZER, JAY; RENDER, BARRY, OPERATIONS MANAGEMENT, 6th ed., © 2001. Reprinted and Electronically reproduced by permission of Pearson Education, Inc., New York, NY.