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Ms. Rieder's Event Planning Project

This is a sample project for Algebra 1.
by

Jane Rieder

on 4 April 2014

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Transcript of Ms. Rieder's Event Planning Project

Ms. Rieder's Earth Day Event
Break-Even Point
What and why?
I propose a fundraiser to celebrate Earth Day. We could attend an Earth Day event and sell healthy snacks. The purpose is to raise money to plant trees in deforested areas of the world.

This event is important to me because I love snacks and I love trees. It's important to the planet because trees help to maintain a healthy environment.
Revenue Analysis

Total Revenue for the event
Selling Apple Juice
Accepting Donations
Revenue Analysis
Selling Trail Mix
I plan to charge $1.50 for each apple juice.
I predict that 80% of customers will buy an apple juice.
Expected revenue = $1.20 per customer
I plan to charge $1.50 for each bag of trail mix.
I predict that 75% of customers will buy a bag of trail mix.
Expected revenue = $1.13 per customer
I also plan to accept donations.
I predict that each person who donates will donate about $5.00, and that 10% of customers will donate.
Expected revenue per customer = $0.50
$1.20 + $1.13 + $0.50

= $2.83 per customer
Revenue Equation
Revenue Graph
My calculations show that I can expect revenue of about $2.83 per person from this event.

That means that I can write a revenue equation like this:
y = 2.83x
(y = money I make and x = number of customers)
Total Costs of the Event
Advertising Posters
Trail Mix
Table
Cost Analysis
Apple Juice
costs $19.30 for 24 10-ounce bottles
is a variable cost because it depends on the number of customers
each case can serve 24
cost per customer = $0.80
costs $18.17 for 24 2-ounce bags
is a variable cost because it depends on the number of customers
each package can serve 24
cost per customer = $0.76
costs $0 because I can borrow it from home
is a fixed cost because it doesn't depend on the number of customers
cost $6.99 for a pack of 10 poster papers
this is a fixed cost because it doesn't depend on the number of customers
I can borrow markers and other supplies from home
Total fixed cost: $6.99

Total variable cost: $1.56 per customer
Cost Equation
Graph of Cost Equation
Cost Equation
Explanation of Cost Equation Graph

The slope of this equation is 2.83. This means that for every additional customer served, I earn $2.83.

The y-intercept of this graph is 0. This means that if 0 customers buy anything, I will earn $0.
The equation that models the cost of my event is:
y = 1.56x + 6.99

y stands for the amount of money I spend.

x stands for the number of customers.
The slope of this line is 1.56, which means that for each additional customer, I will have to spend $1.56.
The y-intercept is 6.99, which means that my fixed cost is $6.99. (Even if 0 customers show up, my fixed cost would still have to be paid.)
I want to know how many customers I have to serve in order to break even. I can answer that question in 2 different ways.
To solve for the break-even point, I can use algebraic or graphical methods.
Algebraic method:
Graphical Method:
The Break-Even Point
My cost equation is y = 1.56x + 6.99.
My revenue equation is y = 2.83x.

I want to find the place where the cost and revenue are EQUAL, so I can set the two equations equal to each other, like this:

1.56x + 6.99 = 2.83x --> then I'll solve for x.
-1.56x -1.56x

6.99 = 1.27x
This means I will


need 6 customers
6.99/1.27 = x
to break even.


5.5 = x

Graph the 2 equations and see where they cross.
The point of intersection is the break-even point, because that's the place where cost and revenue are equal.


x = number of people
y = amount of money
x = number of people
y = amount of money
x = number of people
y = amount of money
Business Plan and Profit Analysis
Number of Customers
Profit Equation
Graph of all 3 equations
I believe my event will serve a total of about 20 people. If 20 people attend my event, my costs will be:
1.56(20) + 6.99 = 31.20+6.99 =
$38.19
My revenue will be:
2.83(20) =
$56.60

Since profit is revenue minus cost, my profit will be:

56.60
-
38.19
=
$18.41
I can also create an equation to find the profit for any number of people who attend my event.

Since profit is revenue minus cost, I can subtract the cost equation from the revenue equation to find the profit.

profit = 2.83x - (1.56x + 6.99)
profit = 1.27x - 6.99
The green line represents the profit from my event. I noticed that the profit is $0 when x = 5.504, which matches the break even point that I found in the previous section.
Image credit: Nevit Dilmen
Full transcript