Essay 3: Mathematics of a Small Business--Turf Plus

Turf Plus,, is a service lawn care company based in Provo, UT. A small business that specializes in treatments of fertilizer, herbicide, and insecticide, guaranteeing their customer lawns’ stay healthy, green, and weed free. Like any business, Turf Plus uses mathematics to ensure operating costs are below revenue gained in order to make a profit. Much is to be considered when calculating the many costs that go into a business, therefore each position within the company must be trained sufficiently so that time spent will be both productive and efficient. By which, operating costs are minimized and revenue is maximized.

Mathematics is prevalent in every position at Turf Plus. First, I will give a brief overview of the company main concern and provide basic formulas used for the services provided. I will then examine the mathematics needed in each of the following employee positions: sprayer, appointment confirmer, office manager, and owner. By so doing, you will come to a better understanding of how mathematics is used in the operation of this small business.

Company's Main Concern

In order to guarantee a healthy, green and weed free lawn, much is to be considered. How much fertilizer is necessary to make sure the lawn will green, but not burn? How much herbicide is needed to control your broad-leaf weeds? When insects are present, how big of an area needs to be sprayed to make sure they are killed? Most importantly, how often does a treatment need to be applied in order to maintain that healthy, green and weed free lawn? Asking these simple questions tends to present somewhat more complicated answers. Through experience and basic math, the owner of Turf Plus has created a chemical fill chart for his employees to follow.

The chemical fill chart lists all products used by the company. It provides basic formulas for each solution to be mixed to guarantee the advertisement of “a healthy, green and weed free lawn.” Along with the ratios of chemical to water, the chart provides the amount of area that each product will cover. For example, 1 gallon of solution will cover 500 square feet of lawn. This chart is used daily as the sprayers calculate the amount of gallons they will be spraying on their route; which will be discussed in more detail below.

Sprayer Position

Sprayers are responsible for spraying a customer’s lawn with fertilizer, herbicide, and insecticide, when applicable. If too much fertilizer is applied, too heavy, then the lawn will burn. If not enough, too light, then the lawn will not green up. Herbicide is a bit different. If you apply a heavier amount of herbicide, it will not kill more weeds; however, it will cost the company more money, because of the expense of the product. If there are difficult weeds in a lawn to kill, then the sprayer has a separate hand tank with a more powerful herbicide to apply, when necessary. Again, applying the stronger solution would cost more money. Insecticide is the most expensive and only applied if a lawn had insects. It is not a preventative, like herbicide.

When a sprayer applies for employment at Turf Plus, they are given a short math test. The purpose is to verify the applicant understands basic math because it is used as part of their daily job. For example, they are asked how many ounces are in one gallon. This is important to know as they refer to the chemical fill chart. More than likely, they will be filling a tank of 300-400 gallons of solution and would need to calculate how many ounces of product needed so many gallons.

They are also asked to provide the formula of a square, circle, and triangle. This is used daily as they provide estimates to new customers. Given that landscaping of most lawns are unique and different, it is important to know the area of each shape to give a correct approximation. To do this, the sprayer will visualize a lawn into squares, rectangles, circles or triangles measure it and add each area together to give a total approximate square footage. Once they have a square footage, they are able to provide pricing for the customer and know how much solution to spray on the lawn.

Each day, a sprayer will receive a route sheet with individual invoices for the customers which he is spraying that particular day. The route sheet contains the information needed for the sprayer to determine how many total gallons of solution will be needed for the day. The invoice contains instructions if individual customers have a special need or want (i.e. insects, fungus, etc.). This information is pulled from the company database by using merge fields for information needed. The sprayer will review the route sheet and invoices to help determine the day's work. Once the total number of gallons needed is determined, the sprayer refers to the chemical fill chart to calculate how much of each product is required. For example, if the sprayer has a total of 350 gallons to be sprayed, he will need to mix 7 bags of nitrogen (40-0-0), 8.0 quarts of MecamineD, and 2.1 pounds of cavalcade with 350 gallons of water.

To guarantee the sprayer will use the correct amount of solution per lawn, each truck has been calibrated so that 4 gallons will come out of the hose every minute. This is done at the beginning of each season as the sprayer sprays for 1 minute into a 5 gallon bucket and the nozzle is adjusted accordingly to make sure it meets the criteria. Also, a sprayer is assigned the same truck each day and the same 3 areas each week, to be able to develop a rhythm and familiarize themselves with the same customers and lawns. This helps in the consistency of work, so that the job can be done efficiently and productively.

The sprayer plans out his day by making work estimates. For example, 12 gallons should only take 3 minutes to spray and cover 3,000 square feet of lawn. The sprayer also needs to calculate the amount of time it takes to pull the hose far enough out to cover the lawn, pulling to the furthest corner away, then spraying and as you reel the hose back in. Thus, if lawn is 3,000 square feet, only needs 12 gallons of spray, and the time it takes to pull out and place the hose is 7 minutes, the sprayer should only be at a house 10 minutes. The routes are given in order therefore the sprayer should not have to backtrack in an area if they followed the route. They sprayer also calculates 5 minutes of drive time to the next house on the route. Then, if the sprayer can get 5 homes done in 1 hour and 15 minutes, if all were 3,000 square feet and used 12 gallons of spray. The calculation being: 5 minute drive between each house plus 3 minutes to spray each yard plus 7 minutes to pull hose in and out at each home, which is 15 minutes per route house multiplied by 5 equals 75 minutes. If they work a 10 hour day, they should be able to finish 40 houses. This calculation being 10 hours times 60 minutes in each hour, equals 600 minutes. Divide that by 15 minutes per house, equals 40 houses. The number of gallons used over the entire day is 12 gallons per house times 40 houses is 480 gallons. However, since they are not all the same size and sometimes more than a 5 minute drive apart, and taking in to account a lunch break, the average number of houses per day is around 17-20. Additionally, the average lawn size is about 7000 square feet.

Throughout the day, the sprayer is assigned points for the service provided. This point system helps the owner know if he is making money and provides a bonus system for the sprayers in order to given them an incentive to work. They sprayer receives 1 point for each estimate, service call, and door collection, 1.33 points per spray (under 20 gallons), 2.66 points per spray (over 20 gallons), and 0.5 points for a door collection dropped off, but not collected. According to this route sheet, the sprayer did 6 houses over 20 gallons, 17 houses under 20 gallons, 2 service calls, 1 door collection drop-off, and 1 estimate. So, our production point total is 6 x 2.66 + 17 x 1.33 + 2 x 1 + 1 x 0.5 + 1 x 1 = 15.96 + 22.61 + 3.5 = 42.07. We multiply this by the area factor (see Owner section): 42.07 x 0.43 = 18.1. We divide this number by the number of hours worked that day. This sprayer had a long shift and worked 11.5 hours. Thus, 18.1/11.5 = 1.57. The 1.57 is the level of productivity for the sprayer that day.

The owner of Turf Plus has created a Bonus Chart to help calculate bonuses. Each pay period, the appointment confirmers call customers to give ratings to the company and in particular to the company. Using a scale from 1-10 with 10 being the best. Therefore, the bottom row of the chart 8.6 up to 10.0 is and average ratings from customers that each sprayer receives. In order to qualify for a bonus, the individual sprayer must be receiving a rating of 8.6 or higher.

The left hand column is the productivity rate the sprayer receives on a daily basis, ranging from 1.00 up to 1.20. The productivity is calculated by the sprayer each day on the route sheet. He takes the total number of points received (1.33 pt. per spray, 1 pt. per estimate, etc.) multiplies it by the area factor which will give him his “earned hours”. He then divides that number by the total hours worked (from the time he clocked in and clocked out) and receives his productivity for the day. The bonus is received as an average of each day is taken and the sprayer is given and overall productivity. For example, if over the course of the 2 week pay period, the sprayer’s average productivity was 1.07 and he had an average customer rating of 9.7, then his bonus would be .74 raise each hour worked. Therefore, if he worked a total of 72 hours, his bonus would be 72 x 0.74 or $53.28.

The top row represents a total bonus from $5.00 up to $12.00. This is given when a sprayer has a daily productivity of 1.20 and matches up with the customer rating. For example, if a sprayer had 8 daily productivity of 1.20 and received an average customer rating of 9.7, then his bonus would be 8 x $10.50 or $84.00.

Unfortunately for the sprayer, he will receive only one of the bonuses described above. Therefore, it would be better for a sprayer to have a higher daily productivity of 1.2 rather than an average productivity of 1.07 because he will receive a higher bonus. Using this bonus system, helps guarantee the owner that his employees are working hard and giving quality service. It is the office manager’s responsibility to process payroll and also calculates the averages for each individual sprayer and assigns the proper bonus. So once again, this goes to show that math is used in all aspects of this small business.

The Appointment Confirmer

The appointment confirmer is in charge of contacting the customers and setting up appointments with them. They use math to determine if the company is making money. They calculate how many calls per hour they make. The important number they keep track of are the "okays," i.e., it is okay to come and spray in the next week or so. They count how many “okays” they receive, then divide that number by how many total hours they spent calling. The company needs 10 okays per hour for it to make money.

The Runners

When more customers are needed, the company employs runners. The runners have the job of going house to house in each neighborhood and pass out flier advertisements for the company. The company needs to deliver a certain number per hour which will cause a certain number of people to sign up for service. The company hopes that enough new people sign up to make a profit after paying for the cost of flyer and runner. For Turf Plus, the details on the mathematics of this effort have not been explored for optimability.

The Office Manager

The office manager uses math when she calculates payroll and the price to charge customers based on the area of their lawn. She uses a database to help keep track of the mathematics discussed in this essay in order to do many of the calculations automatically.

The Owner

The owner of the business uses mathematics to help him make sure his company is making money. Over the years, he has developed key indicators, which include the productivity factor for the sprayers, described above, and the rule of thumb of 10 okays per hour for the appointment confirmers. Additionally, the owner of the company has created what is called an Area Factor for each of the 15 assigned areas sprayed each week. Considered in assigning each factor is average drive time from each customer’s home and average lawn size. In talking with the owner, he would like to figure a “mathematical equation” for assigning these numbers, but nothing has worked better than experience. The area factors are used at the end of each day, when a sprayer is calculating his productivity on the route sheet. They are as follows:

Area Factor
1 0.43
2 0.41
3 0.41
4 0.39
5 0.39
6 0.39
7 0.40
8 0.42
9 0.44
10 0.46
11 0.46
12 0.43
13 0.43
14 0.48
15 0.50

Finally, if the sprayers did not have a production level above 1.0, according to the owners production level system, he was losing money. In that event, he would concentrate on training the employee to work more efficiently.