In this unit, you will be exploring a number of useful math topics that will be used in our first Unit Project. This project will incorporate elements from all 4 units and will be worked on a few pieces at a time. The different parts can be submitted to your teacher for safe keeping, or can be kept by yourself. In either case, a complete, finished project will be due at the end of the Unit.

**Unit 1 Project: The Menu**

As part of your unit project, you will be developing a menu for a restaurant and presenting some data that we collect from our restaurant. The first step is to come up with a name for your restaurant and develop a menu.

Your menu should include:

- a list of drinks
- a minimum of 2 appetizers that customers can choose from
- a minimum of 3 entrees (main meals) that customers can choose from
- a minimum of 2 desserts that customers can choose from
- a description of each item and a cost for each

Any sucessful restaurant wants some feedback from the public before they open. What if you choose to put an item on your menu that nobody wants to buy? You could be wasting money buying ingredients! Today, you are going to survey some members of the public to see which items on your menu will be the most popular, and then you will create a visual representation of your results using an appropriate graph.

- Create a tally sheet for recording your data. This could simply be a table with space to write check marks beside each item.
- Show your proposed menu items to people and ask them what they would choose if they were to choose an item from each category. You should also record the number of people that you surveyed!
- Create an appropriate graph showing how many people chose each item from the menu and make 2 conclusions based on this graph.
- Write a short paragraph explaining which graph you chose to show your survey results and explain why you chose that method.
- Create circle graphs to compare the choices for appetizers, entrees, desserts and drinks. Note: You will need to include 4 separate circle graphs and explain how you convert your fractions to percents

While graphs are great visual ways to show your data, sometimes it is possible to make misleading graphs.

You have conducted a survey using your restaurant menu to find out what choices are more popular for appetizers, entrees, deserts and drinks. You will be constructing 3 misleading graphs to misrepresent the data found in your survey.

- Construct a misleading graph using your data to make the most popular appetizer look way more popular. Explain (using 2 or 3 sentences) how you made the graph look misleading.
- Contstruct a misleading pictograph to make the less popular dessert look more popular than the other desserts. Explain how you made this graph look misleading.
- Create a misleading graph using your entrees. Do not use the same method of making a misleading graph as you used in part 1 or part 2. Explain how you made this graph look misleading.

By now, you have selected a menu and have surveyed some people for their responses. However, it would be nice to be able to estimate what your sales will be in a day, or in a month. You will be using your survey data to make some projections based on this information.

- Decide how many seats your restaurant will have. You will need to choose whether you are opening a small, quaint restaurant (like Ozzie's Deli in Tsawwassen 3-5 tables), a mid sized restaurant that could service a small community (like Mario's Kitchen 6-10 tables) or a much larger restaurant (like White Spot or larger! 11-50 tables!). We will assume that each table can seat 4 people.
- Decide how many hours your restaurant will be open for, as this will determine how many seatings you can manage in a day. Many restaurants assume that people will sit down for 2 hours while eating dinner, although some people may stay longer, and many will leave earlier. Based on a 2 hour seating, the number of tables and the length of your hours of operation, calculate the maximum number of people your restaurant could serve in a day. Using math symbols and a few sentences, explain how you calculated your maximum occupancy. Then, use this number to also calculate:
- 50% occupancy: the number of people that you can seat if you are half full

- Use proportional reasoning to determine how of each menu item you would need to prepare to meet your full occupancy and 50% occupancy numbers. For example, if you determine that your full occupancy is 120 customers in a day, calculate how many of each menu item you could expect to sell if you had 120 customers a day and if you had 60 customers in a day.

By the end of this part of your assignment, you should have:

- A short sentence explaning how large your restaurant is and how many tables it has
- A calculation that shows how many people you can serve at one time
- A calculationg that shows how many people you could serve in a day as well as an explanation of how you determine this amount
- Your 50% occupancy number
- A set of numbers showing how many of each menu item you would serve based on full occupancy and 50% occupancy. You should decide what might be the best way to present these numbers. You will need to include an explanation of how you calculated one of these numbers.

Now that you have your restaurant planned out, it's time to start taking care of the details, like designing and producing a menu.

We will be designing rectangular menus with a diagonal length of 25cm, 30cm or 35cm. You will need to decide what lengths and widths will make this diagonal.

- Use your knowledge of the Pythagorean relationship to find 2 different lengths and widths that will produce a diagonal length of 25cm, 30cm or 35cm.
- Show your calculations for these 2 menu sizes
- Create a production version of your menu using one of the dimensions that you have found.

- You have just found out that ____________________ is your long lost cousin, and is coming over to visit (how exciting)! You decide to treat them to a meal in your restaurant, but your cousin pays the bill. You, accept, but insist on paying the tip. Remember that a typical gratuity is to tip 15% of the value of the meal (before taxes) or higher
- Order lunch for you and your cousin from your menu, and include the costs for each item
- Subtotal the entire bill (you can use a calculator for this part)
- CALCULATE the amount of tax (GST is 5%) that you needed to pay on your meal as well. Remember, that tax is based on the amount you pay
- ESTIMATE the tip that you need to leave. Explain how you got your estimate. State the percent you are planning on leaving for your tip.

After sharing a meal with your long lost cousin, you remember that you have a discount card that can be applied to the cost of the meal!

- Discounted prices are always used to calculate tax (usually just 5% GST)
- Regular prices are used to calculate the tip / gratuity ( you pretend there was no discount at all ).

You’ve already calculated the tip (from the Take Your Cousin to Lunch Assignment), so you will only need to calculate the amount of the bill.

- You have a 10% off the value of the meal coupon. Determine your bill including the discount, and GST but not including the tip.
- You have a “Buy one entrée, get a second entrée of equal or lesser value for free” coupon. Determine the cost of your meal including the discount. What was the actual percent savings?