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Sagot :
### Part A: Displaying the Offers in the Same Format
Let's convert all offers into tabular format for easier comparison.
#### 1. Hoodies R Us:
Hoodies R Us provided a pricing table directly, which is as follows:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Hoodies} & \text{Price (dollars)} \\ \hline 20 & 130 \\ \hline 40 & 200 \\ \hline 60 & 270 \\ \hline 80 & 340 \\ \hline 100 & 410 \\ \hline 120 & 480 \\ \hline 140 & 550 \\ \hline \end{array} \][/tex]
#### 2. Company B's Description:
Company B charges a base fee of \[tex]$8 plus \$[/tex]6 per hoodie.
[tex]\[ \text{Cost} = 8 + 6 \times (\text{Number of Hoodies}) \][/tex]
Calculating for 20 to 200 hoodies:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Hoodies} & \text{Price (dollars)} \\ \hline 20 & 128 \\ \hline 40 & 248 \\ \hline 60 & 368 \\ \hline 80 & 488 \\ \hline 100 & 608 \\ \hline 120 & 728 \\ \hline 140 & 848 \\ \hline 160 & 968 \\ \hline 180 & 1088 \\ \hline 200 & 1208 \\ \hline \end{array} \][/tex]
#### 3. Company C's Equation:
Company C uses the equation [tex]\( C = 10q + 20 \)[/tex], where [tex]\( q \)[/tex] is the number of hoodies.
Calculating for 20 to 200 hoodies:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Hoodies} & \text{Price (dollars)} \\ \hline 20 & 220 \\ \hline 40 & 420 \\ \hline 60 & 620 \\ \hline 80 & 820 \\ \hline 100 & 1020 \\ \hline 120 & 1220 \\ \hline 140 & 1420 \\ \hline 160 & 1620 \\ \hline 180 & 1820 \\ \hline 200 & 2020 \\ \hline \end{array} \][/tex]
#### 4. Company D's Graph Interpretation:
Company D's pricing structure appears to follow the equation [tex]\( C = 15q - 50 \)[/tex].
Calculating for 20 to 200 hoodies:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Hoodies} & \text{Price (dollars)} \\ \hline 20 & 250 \\ \hline 40 & 550 \\ \hline 60 & 850 \\ \hline 80 & 1150 \\ \hline 100 & 1450 \\ \hline 120 & 1750 \\ \hline 140 & 2050 \\ \hline 160 & 2350 \\ \hline 180 & 2650 \\ \hline 200 & 2950 \\ \hline \end{array} \][/tex]
### Part B: Comparing and Explaining the Choices
#### Comparison:
1. Hoodies R Us has specific rates for increments of 20 hoodies and is the most affordable option up to 140 hoodies.
2. Company B's costs increase steadily with a fixed initial charge and per-hoodie fee, making it the cheapest option for higher quantities beyond the offerings of Hoodies R Us.
3. Company C is more expensive than Company B for all quantities due to its higher per-hoodie cost and a fixed fee.
4. Company D has the steepest increase due to the highest per-hoodie cost and a fixed discount, making it the least favorable financially for nearly all quantities.
#### Analysis by Quantity:
- 20 hoodies: The best option is Hoodies R Us at \[tex]$130. - 40-140 hoodies: Continue with Hoodies R Us, which ranges from \$[/tex]200 to \[tex]$550. - 160-200 hoodies: Company B becomes beneficial at 160 hoodies costing \$[/tex]968 compared to Company C at \[tex]$1620 and Company D at \$[/tex]2350.
Overall, Hoodies R Us is the best choice when ordering up to 140 hoodies, and Company B is more cost-effective for larger orders beyond 140 hoodies.
#### Reasoning:
- Fixed Costs: Companies like Company B and Company C have fixed costs that impact initial lower quantities more significantly.
- Per-Hoodie Cost: The rate per hoodie influences overall cost heavily, which makes Company B preferable for higher quantities due to its lower per-unit cost compared to Company C and Company D.
These comparisons allow us to decide based on minimizing expenses depending on the quantity of hoodies ordered.
Let's convert all offers into tabular format for easier comparison.
#### 1. Hoodies R Us:
Hoodies R Us provided a pricing table directly, which is as follows:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Hoodies} & \text{Price (dollars)} \\ \hline 20 & 130 \\ \hline 40 & 200 \\ \hline 60 & 270 \\ \hline 80 & 340 \\ \hline 100 & 410 \\ \hline 120 & 480 \\ \hline 140 & 550 \\ \hline \end{array} \][/tex]
#### 2. Company B's Description:
Company B charges a base fee of \[tex]$8 plus \$[/tex]6 per hoodie.
[tex]\[ \text{Cost} = 8 + 6 \times (\text{Number of Hoodies}) \][/tex]
Calculating for 20 to 200 hoodies:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Hoodies} & \text{Price (dollars)} \\ \hline 20 & 128 \\ \hline 40 & 248 \\ \hline 60 & 368 \\ \hline 80 & 488 \\ \hline 100 & 608 \\ \hline 120 & 728 \\ \hline 140 & 848 \\ \hline 160 & 968 \\ \hline 180 & 1088 \\ \hline 200 & 1208 \\ \hline \end{array} \][/tex]
#### 3. Company C's Equation:
Company C uses the equation [tex]\( C = 10q + 20 \)[/tex], where [tex]\( q \)[/tex] is the number of hoodies.
Calculating for 20 to 200 hoodies:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Hoodies} & \text{Price (dollars)} \\ \hline 20 & 220 \\ \hline 40 & 420 \\ \hline 60 & 620 \\ \hline 80 & 820 \\ \hline 100 & 1020 \\ \hline 120 & 1220 \\ \hline 140 & 1420 \\ \hline 160 & 1620 \\ \hline 180 & 1820 \\ \hline 200 & 2020 \\ \hline \end{array} \][/tex]
#### 4. Company D's Graph Interpretation:
Company D's pricing structure appears to follow the equation [tex]\( C = 15q - 50 \)[/tex].
Calculating for 20 to 200 hoodies:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of Hoodies} & \text{Price (dollars)} \\ \hline 20 & 250 \\ \hline 40 & 550 \\ \hline 60 & 850 \\ \hline 80 & 1150 \\ \hline 100 & 1450 \\ \hline 120 & 1750 \\ \hline 140 & 2050 \\ \hline 160 & 2350 \\ \hline 180 & 2650 \\ \hline 200 & 2950 \\ \hline \end{array} \][/tex]
### Part B: Comparing and Explaining the Choices
#### Comparison:
1. Hoodies R Us has specific rates for increments of 20 hoodies and is the most affordable option up to 140 hoodies.
2. Company B's costs increase steadily with a fixed initial charge and per-hoodie fee, making it the cheapest option for higher quantities beyond the offerings of Hoodies R Us.
3. Company C is more expensive than Company B for all quantities due to its higher per-hoodie cost and a fixed fee.
4. Company D has the steepest increase due to the highest per-hoodie cost and a fixed discount, making it the least favorable financially for nearly all quantities.
#### Analysis by Quantity:
- 20 hoodies: The best option is Hoodies R Us at \[tex]$130. - 40-140 hoodies: Continue with Hoodies R Us, which ranges from \$[/tex]200 to \[tex]$550. - 160-200 hoodies: Company B becomes beneficial at 160 hoodies costing \$[/tex]968 compared to Company C at \[tex]$1620 and Company D at \$[/tex]2350.
Overall, Hoodies R Us is the best choice when ordering up to 140 hoodies, and Company B is more cost-effective for larger orders beyond 140 hoodies.
#### Reasoning:
- Fixed Costs: Companies like Company B and Company C have fixed costs that impact initial lower quantities more significantly.
- Per-Hoodie Cost: The rate per hoodie influences overall cost heavily, which makes Company B preferable for higher quantities due to its lower per-unit cost compared to Company C and Company D.
These comparisons allow us to decide based on minimizing expenses depending on the quantity of hoodies ordered.
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