Reference no: EM133028685

Solving a System of Linear Equations Project

‘Dragon's Den'

You and your group are hoping to start a business and are going to invent a product or re- invent an existing product to sell. You must prepare a 5-10 minute presentation to ‘The Dragons' on your product based on the outline below. If your presentation is successful, the Dragons will invest in your product and you will be able to start your business.

Background Information:

Let's begin by defining four basic (and often misunderstood) terms that affect cash flow in every business:

• Cost: Money you pay, directly or indirectly, to produce a product or service. Costs include labor (your own labor and any hired help), rent, taxes, utilities, production inputs, equipment depreciation, etc.

• Price: Money you receive from a customer for a product or service. Your price should include all your costs, plus some extra money to keep (profit, or "return to management").

• Revenue: Money you receive from all sales of your products and/or services (also known as gross income). Revenue should cover all your business costs and give you some extra money to keep (profit).

• Profit: Money you get to keep from all sales of your product or services, after all your costs are paid (also known as net income). Profits allow you to buy your daily necessities, invest back into the business, save for the future, and take that vacation you have been planning!

Let's look at the graph below:
The blue line (revenue) represents the amount of money you will make as you sell more units of your product. Therefore it increases everytime you sell your product.

The red line (total cost) shows the total cost to your business based on a fixed start-up cost of $4000 and the cost of making your product.

In order to determine how much money you will need to borrow from me, you need to be able to find where the costs of the business exactly equals the revenue the business brings in. This point where the business ‘breaks even' (called the ‘break-even point') will be where those two lines intersect. Therefore, on the example above, the point at which the company breaks even would be when they have sold around 571 or 572 units.
When the cost = revenue you will get an ordered pair. This ordered pair of the break-even point will represent the number of units of the product that have been produced and sold, and the amount of money that will have been taken in and paid out when cost equals the revenue.
Make sure you note that: until you have reached the break-even point, the business is losing money. Why? Because at all the points on the line up until this point, the costs are higher than revenue. After the break-even point, the business makes money. Why? Because revenues are higher than cost.
You are going to need to prepare a presentation for ‘the Dragons' (the potential investors) to convince us to give you a loan for your start-up costs until you start generating a profit.

Instructions:

Step 1: Product Development
Your first step is to come up with a product to sell. Consider the following as you create your product:

- What is the purpose of your product? What is your HOOK? (i.e. what makes your product different from everyone else?)
- Who is the target audience/market for your product?
- How much are you thinking of selling it for? Where will you sell it?
- How much will it cost to make each product?
- What are the start-up costs for your business?
You have approximately 1.5 hours to work on your product development. You can use resources on the internet to help you create your product, find out how much it will cost you to make it, and how much you should reasonably sell it for. Please have the above questions answered within your group before you move on to step 2.

Step 2: Create & Solve your System of Linear Equations
1. You should have the following information from your initial research:
- the amount it will cost to start-up your business
- the amount it will cost to make each product
- the amount you are going to sell your product for
2. From this data, you are going to create two equations:
Equation 1: Cost: y = mx + b
Where: y = total amount of money it will cost you
m = cost for producing ‘x' amount of products b= fixed start-up cost
Equation 2: Revenue: y = (price) x
Where: y = total amount of money you will make
(price) = the amount you are charging for each product x = number of products you will sell

3. Write down your system of linear equations.
4. Solve your system of equations using the three methods that we have discussed in class: the Graphing Method, the Substitution Method, and the Elimination Method.

Step 3: Create Your Presentation
In order to convince the Dragons that you deserve their investment, you will need to have the following:
- A strong hook and a strong description of the product including information about the use of the product and the target audience (market) who will want to purchase this product and why.
- A clear explanation of the start-up (fixed) cost to start this business, the cost to make the product, and the cost to continue running the business.
- A convincing proposition including the exact amount of money you are asking for (that is, the amount of money represented by the break-even point for the price you select) and a clear explanation of the amount of profit you expect to make over the next year.
- A description of what the Dragon (your potential investor) will get by investing in you! (i.e. special benefits? A percentage of the profit?)
- You will be graded on the mathematics of finding your break-even point using the three methods (Graphing
- You will also be graded on your creativity, presentation style and group effort

Product:
In order to convince the Dragons that you deserve their investment, you will need to have the following:
- A strong hook and a strong description of the product including information about the use of the product and the target audience (market) who will want to purchase this product and why
- A clear explanation of the start-up (fixed) cost to start this business, the cost to make the product, and the cost to continue running the business.
- A convincing proposition including the exact amount of money you are asking for (that is, the amount of money represented by the break-even point for the price you select) and a clear explanation of the amount of profit you expect to make over the next year.
- A description of what the Dragon (your potential investor) will get by investing in you! (i.e. special benefits? A percentage of the profit?)

- You will also be graded on your creativity, presentation style and group effort.

Attachment:- Linear Equations Project.rar