Oumy Samba - Comparing Functions Activity.pdf

Question

How rnuch is the set up charge? , How rnuch does each shirt cost? Write a function that represents the cost of ordering shirts here. Shir+s name Comparing Func+ions — T-Shir+ Companies The eighth grade is planning to order official shirts. The Student Council is researching shirt printers to find the best price for the shirts. Each company has a set-up charge and a cost per shirt. Analyze each function and then answer the questions to help find the best deal. Cost of Printing - Stand Out Shirts Impressive Imprn±s Irnpressive Imprints sent a brochure with the Awesome Apparel The Student Council found this inforrnation on following table: number oP Shlr+s 5 20 50 cos+ $100 $157.50 $330 $675 Awesome AppareI's website. number of Shir±s 5 20 50 $200 $245 $380 $650 600 400 200 600 4 3 o 10 20 30 40 Number of Shirts How rnuch is the set up charge? How rnuch does each shirt cost? Write a function that represents the cost of ordering shirts here. How much is the set up charge? How much does each shirt cost? Write a function that represents the cost of ordering shirts here. Lo+s oP Logos Cost of Printing - Lots of Logos 600 ooooooay 2 200 o 10 20 30 40 Number of Shirts How rnuch is the set up charge? How much does each shirt cost? Write a function that represents the cost of , ordering shirts here.
$100

$11.50

Cost(N)=100+11.50

$200

$9

0

25

y=9x+200

$15

y=15x+0

$13

y=13x+25

Ques±ions 1. 2. 3. 4. Which company charges the least for each shirt? The rnost? Which company has the lowest set-up charge? The highest? The Student Council decided to order a small batch of 10 shirts for members only to advertise. a. Where should Student Council order 10 shirts? Show your work to explain how you got your answer. b. What would be the difference in price between Stand Out Shirts and Awesome Apparel? The shirts came out great and Student Council received 200 orders for shirts. They decided to check their costs again. a. b. Where should Student Council order 200 shirts? Show your work to explain how you got your answer. What would be the difference in price between Stand Out Shirts and Awesorne Apparel?
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+

100%

Answer 1

To analyze the costs of ordering shirts from different companies, we can define each company's pricing structure based on the information provided in the activity.

1. Stand Out Shirts:

   • Set-up charge: $100
   • Cost per shirt: $11.50
   • Cost function: \[ C(N) = 100 + 11.50N \]

2. Awesome Apparel:

   • Set-up charge: $200
   • Cost per shirt: $9
   • Cost function: \[ C(N) = 200 + 9N \]

3. Lots of Logos:

   • Set-up charge: $15
   • Cost per shirt: $0 (seems to imply no additional charge per shirt).
   • Cost function: \[ C(N) = 15 + 0N = 15 \]

Let's answer the questions based on these functions.

Questions:

1. Which company charges the least for each shirt? The most?

   • Least per shirt costs:
     • Stand Out Shirts: $11.50
     • Awesome Apparel: $9
     • Lots of Logos: $0 (best deal per shirt, but needs to be considered with setup charge)
   • Most per shirt costs:
     • Stand Out Shirts: $11.50 (most expensive per shirt cost)

2. Which company has the lowest set-up charge? The highest?

   • Lowest set-up charge: Lots of Logos ($15)
   • Highest set-up charge: Awesome Apparel ($200)

3. Where should the Student Council order 10 shirts?

   • Calculate total costs for 10 shirts:
     • Stand Out Shirts: \[ C(10) = 100 + 11.50 \times 10 = 100 + 115 = 215 \]
     • Awesome Apparel: \[ C(10) = 200 + 9 \times 10 = 200 + 90 = 290 \]
     • Lots of Logos: \[ C(10) = 15 + 0 \times 10 = 15 \]
   • Conclusion for 10 shirts: The best option is Lots of Logos at $15, which is the cheapest option.

4. What would be the difference in price between Stand Out Shirts and Awesome Apparel for 10 shirts?

   • Difference: \[ 290 - 215 = 75 \]
   • So, Stand Out Shirts is $75 cheaper than Awesome Apparel for 10 shirts.

5. Where should the Student Council order 200 shirts?

   • Calculate costs for 200 shirts:
     • Stand Out Shirts: \[ C(200) = 100 + 11.50 \times 200 = 100 + 2300 = 2400 \]
     • Awesome Apparel: \[ C(200) = 200 + 9 \times 200 = 200 + 1800 = 2000 \]
     • Lots of Logos: \[ C(200) = 15 + 0 \times 200 = 15 \]
   • Conclusion for 200 shirts: The best option is Awesome Apparel, totaling at $2000.

6. What would be the difference in price between Stand Out Shirts and Awesome Apparel for 200 shirts?

   • Difference: \[ 2400 - 2000 = 400 \]
   • So, Stand Out Shirts is $400 more expensive than Awesome Apparel for 200 shirts.

Summary:

• For 10 shirts, order from Lots of Logos for $15.
• For 200 shirts, order from Awesome Apparel for $2000.
• The differences in costs are $75 for 10 shirts and $400 for 200 shirts when comparing Stand Out Shirts and Awesome Apparel.