Year 9 Mathematics
Project on System of Equations and Inequalities
Option 1
Upon the completion of the new subway station,
NBHIS will need to relocate the e-bike parking
space in front of the west building as the space
will be used for the entrance/exit area of the
station. The school has decided to combine the
parking space together with cars on the other
side of the south gate. In addition to that, the
school management has decided to ask for the
parking fee for both e-bikes and cars with each ebike costs 40% lower than each car does. The
money that is collected will entirely be given to
the security guards as their additional income.
The school has limited space but needs to accommodate people who like to park at school. School
management is now thinking of what the best combination of cars and e-bikes to park in order is to
earn maximum profit.
Your task is to write a letter/proposal to the school management, proposing a design for the parking
lot that will solve the problem, which is how many of each type should be allowed to park to earn
maximum profit.
In order to achieve the solution, you will need to consider the following:
 total area that will be used for the parking lot
 area that is needed by one car
 are that is needed by one e-bike
 number of people (let say teachers) who will be allowed to park
Your letter should consist of:
 background information (space available, space needed by each vehicle, parking fee for each
vehicle, number of people who can park, etc.)
 linear programming problem you come up with
 solution to the linear programming along with all necessary explanations
 design for the parking lot
Reflection:
 why was the use of a system of linear inequalities necessary for this problem?
 What kind of assumptions you had to make?
 What other factors would influence the school’s decision to accept your proposal?
 If you were the school management, would you want to accept the design?
 What do you like about this project?
 Is there anything you would have liked to have done differently?
Option 2
You are going to open your own store. However,
you need to get a business partner in order to get
enough money to start of the business. To show
your potential partner that you are qualified, you
will show her/him the process you go through when
stocking your products. You are currently trying to
decide how much of product A and product B you
want to buy. Product A takes up less space than
product B, but it also yields a smaller profit and you
have only 600ft3 space available.
Assume that there will be no problem selling any
amount of either product.
Steps:
 choose the two products you want to sell (name and describe each product)
 name your store based on the products you want to sell
 decide on a reasonable amount of space that each product will take up in your store
 assign an appropriate amount of profit for each product you are selling
 think of any other constraint that might need to be considered
 write the situation as linear programming problem
 solve the problem
Final product: a 2-3 minutes PPT
Reflection:
 why was the use of a system of linear inequalities necessary for this problem?
 What do you think about the assumption?
 What other factors would influence the person’s decision to become your business partner?
 If you were the one who receive the proposal, would you want to invest in the store?
 What do you like about this project?
 Is there anything you would have liked to have done differently?
Rubrics
Mathematical Reasoning and
Problem Solving
4
3
2
1
Graphs
Mathematical Concepts
Reflection
25%
I use complex and refined
mathematical reasoning to
research and find information
that will lead to constraints for
the linear programming along
with its objective function
15%
My graph of
the feasible
region is clear
and all
important
parts are
accurately
labelled
20%
My justification shows
complete understanding
of the algebraic concepts
used to solve linear
programming problem(s)
and is presented clearly
and persuasively
15%
All
questions
were
answered
and
elaborated
upon.
25%
My work is
presented in a
neat, clear,
organized fashion
that is easy to
read.
I use effective mathematical
reasoning to research and find
at least two constraints for the
linear programming along with
its objective function
My graph of
the feasible
region is clear
and most
labels are
accurate
My justification shows
substantial understanding
of the algebraic concepts
used to solve linear
programming problem(s)
Most
questions
were
answered
and
elaborated
upon.
My work is
presented in a
neat and
organized fashion
that is usually
easy to read.
I show some evidence of
mathematical reasoning to
research and find some
constraints for the linear
programming and evidence of
identifying the objective
function
My graph of
the feasible
region is
somewhat
inaccurate
My justification shows
some understanding of
the algebraic concepts
needed to solve linear
programming problem(s)
Only few
questions
were
answered
and there is
an attempt
to elaborate
upon.
My work is
presented in an
organized fashion
but may be hard
to read at times.
I show little evidence of
mathematical reasoning used
to find constraints and the
objective function for the
linear programming
My graphs are
inaccurate,
difficult to
understand, or
are not used
My justification shows
very limited
understanding of the
underlying concepts
needed to solve linear
programming problem(s)
or is not written
Only few
questions
were
answered
and there is
no attempt
to elaborate
upon.
My work appears
sloppy and
unorganized. It is
hard to know
what information
goes together.
Conversion
Total point
1.00 – 1.49
1.50 – 1.99
2.00 – 2.49
2.50 – 2.99
3.00 – 3.49
3.50 – 4.00
MYP Grade (C
and D)
3
4
5
6
7
8
Product