# Algebra Questions

• January 31, 2022/

### Description

The ‘Dragon’s Den’ is a reality television show where entrepreneurs pitch their business ideas in the hopes of securing an investment from the team of investors also known as “The Dragons”.

In this activity, you are an entrepreneur pitching your new idea to the Dragon’s Den. You will need to create one of the following options to pitch your idea:

• Video
• Website
• PowerPoint
• Written Report

You must include all calculations and graphs in whichever method you choose.

## Question 1

Watch this clip from Dragon’s Den to familiarize yourself with the concept of pitching your product to investors

http://www.cbc.ca/dragonsden/pitches/pook-toques

## Question 2

Think of a product you would like to invent. Some of the most successful pitches on dragons den are products created for everyday living that will make consumers lives easier. Have you ever been completing a task and thought there has to be an easier way? Well now is the time to explore that idea! If you are having a hard time coming up with an idea go to the Dragon’s Den website. You may choose to use one of these products from the show or a similar one for your project. Choose an item that will retail between \$5-\$10.

http://www.cbc.ca/dragonsden/pitches/category/season-10/

## Question 3

Now you will need to research (see instructions below) how much your idea will cost per month and create a function in the form of to represent it. Here are the two different monthly costs for operating your new business. Choose the most appropriate fit for your product:

## Question 4

Choose a selling price between \$5-\$10. Suppose on an average month you sell 500 items. For every \$0.15 increase in your price you sell 10 less items.

a) Find a function for Revenue, with respect to the number of price increases. Your function will be R(x)= (number of products sold) x (price). It is important to incorporate that for every \$0.15 in your price you sell 10 less items.

[Hint: First find a function for the number products sold, and a function for the price of the item.]

b) Provide a graph for your Revenue Function.

c) Determine the roots of R(x)and interpret them in the context of the question.

D) Determine the maximum or minimum values of R(x) and interpret them in the context of the question.

e) Determine the domain and range of and interpret them in the context of the question

f) Now create a revenue function with respect to the number of items sold and the new selling price.

## Question 5

Using your Cost and Revenue functions, find the profit function, P(x)=R(x)-C(x)

Provide all of your calculations and a graph of your profit function.

## Question 6

Now that you have your new product and all your calculations complete, it is time to create your pitch to The Dragon’s. Remember you are trying to get them to invest in your product so you will want to include all the selling points from your calculations (such as your maximum profit).

a) You must include all calculations and graphs in whichever method you choose to present your pitch.

b) Be concise, keeping it engaging and to the point (Maximum 5 pages, or 10 slides, or 8 minutes).

## Question 7

Write a short reflection on this assignment (1-2 paragraphs). Were your results realistic?

Were your results realistic? What did you learn from this assignment? What was easy and what was more difficult?