The Pi (π) Club at Math High School was planning a fundraiser to sell pepperoni pizza. A pizza company donated enough ingredients to make the equivalent of 300 extra large pepperoni pizzas (16” diameter). In trying to determine the number of pizzas of each size to make, they surveyed students in the school. Based on the survey, the club decided that more than half of the pizzas they make should be extra large; there would be more large (14” diameter) than medium (12” diameter) and between 40 and 50 small (10” diameter). The club members plan to sell the pizzas for $11(small), $15 (medium), $18 (large), and $20 (extra-large).
Mission:
Design a plan for how many of each type of pizza you think the club should sell. Explain why your plan is a good one for the club to raise funds.
To design a plan for how many of each type of pizza the club should sell, we need to take into consideration the following factors:
1. The survey results: The club decided to make more than half of the pizzas extra large. This means that extra large pizzas should be the majority of the pizzas sold.
2. Variety in sizes: The club also decided to have more large pizzas than medium pizzas, and between 40 and 50 small pizzas. This ensures a range of sizes to cater to different preferences and appetites.
3. Fundraising potential: We want to maximize the potential funds raised by selling pizzas. This can be achieved by focusing on selling pizzas with higher prices.
Based on these factors, here's a plan for how many of each type of pizza the club should sell:
1. Extra large (16" diameter): Since more than half of the pizzas should be extra large, let's aim for around 160 extra large pizzas out of the total 300 pizzas. This will give a good variety of sizes as well as meet the majority requirement.
2. Large (14" diameter): To have more large pizzas than medium, let's aim for around 70 large pizzas. This will ensure that there are enough large pizzas for those who prefer a slightly smaller size than extra large.
3. Medium (12" diameter): Since large pizzas should be more than medium, let's aim for around 60 medium pizzas. This will provide a smaller size option for those who may not want a large pizza.
4. Small (10" diameter): The club decided to have between 40 and 50 small pizzas. Let's aim for the higher end of this range and make around 50 small pizzas. This will give enough small pizzas to meet the minimum requirement.
By following this plan, the club will have a good variety of sizes, with the majority being extra large pizzas. This ensures that they cater to different preferences while still meeting the survey results. Additionally, by selling more medium, large, and extra large pizzas, they will be able to sell more pizzas at higher price points ($15, $18, and $20 respectively), maximizing their fundraising potential.