Quadratic Activities Michael Luo.

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Presentation transcript:

Quadratic Activities Michael Luo

Student Council Snack Line Problem The Student Council at your school has decided that the students need more food choices at lunch. They want to open a snack line during lunch hours to serve the needs of the student body and to allow the Student Council to make money for other school projects. What factors might affect the success of the snack line?

Variables and Functions The success of the snack line depends on many factors such as: Types and quality of snacks sold; Prices of snacks; Snack offerings that appeal to students; Number of people who are available and are willing to run the snack line; Speed at which people can move through the snack line; The quality of the food served in the regular lunch line; These factors are called variables because they can change regularly.

Bags of Chips Sold per Day Potato Chip Problem Price Per Bag Bags of Chips Sold per Day $0.5 542 $0.60 478 $0.70 413 $0.80 330 $0.90 249 $1.00 185

Potato chip problem Describe a relation between price and number of bags of chips sold each day from the data shown in the table. Is this relation reasonable? 2. If Student Council want to sell at least 250 bags of chips each day, when price should they charge?

Potato Chip Problem 3. If Student Council wants to sell at least 300 bags of chips each day, what price should they charge? 4. Find the Function of number of bags sold per day based on selling price per bag, and give the viewing window, and graph the function.

Potato Chip Problem (Maximum Revenue) Price per bag Bags of Chips sold per day Revenue L1 * L2 $0.50 542 $271.00 $0.60 478 $286.00 $0.70 413 $289.00 $0.80 330 $264.00 $0.90 249 $224.00 $1.00 185 $185.00

Potato chip problem 5. If Student Council wants to take in the most money possible, what price should they charge? 6. If Student Council wants to take in at least $275, how many bags of chips do they need to sell? 7. Find the Function of Revenue based on selling price per bag. And graph;

Potato chip problem 8. If Student Council must pay 35 cents for each bag of chips, what price should they charge in order to maximize their profits? 9. How many bags of chips must be sold in order to maximize profit?

#bags of chips sold per day Potato Chip Problem L1 L2 L3 L4 L5 Price per bag #bags of chips sold per day Revenue per day(L1*L2) Cost per day (0.35 * L2) Profit per day (L3-L4) $0.50 542 $271.00 $189.70 $81.30 $0.60 478 $286.80 $167.30 $119.50 $0.70 413 $289.10 $144.55 $0.80 330 $264.00 $115.50 $148.50 $0.90 249 $224.10 $87.15 $136.95 $1.00 185 $185.00 $64.75 $120.25

Summary of regression equations Y1 = -730 x + 914 Linear (L1, L2) Y2 = -792 x^2 + 1004 x – 31 Quadratic (L1, L3) Y3 = -256 x +320 Linear (L1, L4) Y4 = -752 x^2 + 1199 x –329 Quadratic (L1, L5)