Thinking Skills: Critical Thinking and Problem Solving

5.2 Developing models 213

Perfect Pots is a company making decorative

plant pots. Its overheads (rent on premises,

insurance, etc.) are $15,000 per year. There

are four administrative staff (manager,

accountant, sales director and secretary)

earning a total of $85,000 per year. The pots

are made by a number of skilled workers;

each can produce up to 5000 pots a year and

earns $20,000 per year. Materials, power and

so on cost $1000 per 10,000 pots.

How will the company’s profits vary with

the number of pots made and sold and the

selling price of the pots (assuming the

company only makes pots to supply orders)?

Activity

Commentary
The model depends on the number of workers,
and it must be remembered that each one
cannot produce more than 5000 pots per year.
The mathematics of this model are quite
simple, depending only on multiplication,
addition and subtraction. If the number of
workers is n, the number of pots produced and
sold is m and the selling price per pot is p, the
profit can be calculated as follows:

Income = mp

Expenditure = 100,000 + 20,000n +

1000

10 000

m

,

Profit = mp – 100,000 – 20,000n – 10 m

The table on the next page shows how this varies,
assuming the number of workers employed is
controlled by the number of pots produced.
This type of model is useful to the
accountant and sales director in producing
sales targets. This also leads to the type of
‘what if?’ analysis that is commonly used in
economics. Note that there are points at
which selling extra pots means employing an
extra worker, which can lead to a fall in profits.
The next activity requires the creation of a
relatively simple model and is a good
introduction to modelling.

Greenfinger Garden Services (GGS) offer a

range of garden maintenance tasks, including

lawn maintenance. They charge one rate per

square metre for mowing lawns and a different

rate per linear metre for trimming the edges.

1    Germaine has a rectangular lawn 5 m by

4 m. GGS have been charging him $42

for mowing and trimming the edges of

his lawn. He now wants to put a 2 m by

2 m flower bed in the middle of his lawn,

and has asked GGS how much the lawn

maintenance charge will be when he has

done this. The new lawn is shown below:

Flower bed

4 m

5 m

2 m

2 m

GGS have quoted $51 for mowing and

trimming the edges on his new lawn.

By how much has the edge length been

increased on the new lawn?

2    In order to run their business efficiently,

GGS need a general method for calculating

the amount they will charge for other sizes

or shapes of lawn. Develop a formula or

general rule for calculating the charge for

any shaped lawn (assuming it has right-

angled corners).

3    They have been asked to quote for a new

job. They have measured the lawn and it is

shown in the diagram below. What would

be the charge for this lawn?

8 m

8 m 3 m

4 m

Activity