The Students Councils Found this InforMation on awesome apparel's website

Question

Number of shirts:0,5,20,50
Cost:$200,$240,$380,$650

How much is the set up charge?_
How much does each shirt cost?_
Write a function that represents the cost of ordering shirts here.______

Answer 1

To analyze the information provided from Awesome Apparel's website, we can derive the setup charge and the cost per shirt using the data.

Given Data:

• Number of shirts: 0, 5, 20, 50
• Cost: $200, $240, $380, $650

Step 1: Determine the Setup Charge

The setup charge is the cost incurred when ordering shirts, regardless of quantity. We can find the setup charge by examining the cost when no shirts are ordered:

• When 0 shirts are ordered, the cost is $200. This indicates that the setup charge may be $200, since there are no shirts in this order.

Step 2: Determine the Cost per Shirt

To find the cost per shirt, we can calculate the difference in cost as the number of shirts increases, removing the setup charge from the total cost.

• For 5 shirts: \[ \text{Cost} = 240 \] \[ \text{Cost Without Setup Charge} = 240 - 200 = 40 \quad \text{(for 5 shirts)} \] \[ \text{Cost per shirt} = \frac{40}{5} = 8 \]

• For 20 shirts: \[ \text{Cost} = 380 \] \[ \text{Cost Without Setup Charge} = 380 - 200 = 180 \quad \text{(for 20 shirts)} \] \[ \text{Cost per shirt} = \frac{180}{20} = 9 \]

• For 50 shirts: \[ \text{Cost} = 650 \] \[ \text{Cost Without Setup Charge} = 650 - 200 = 450 \quad \text{(for 50 shirts)} \] \[ \text{Cost per shirt} = \frac{450}{50} = 9 \]

Looking at the calculations, it seems there’s a discrepancy in the per shirt cost as the cost per shirt for 5 shirts is $8, whereas for more shirts it settles around $9. Therefore, we may conclude that the cost structure of shirts varies with quantities.

Conclusion:

• Setup Charge: $200
• Cost per Shirt: $8 for the first order (5 shirts) and then $9 for larger orders.

Step 3: Write a Function

To express the cost function mathematically, a piecewise function can be written to represent the cost based on the number of shirts ordered:

\[ C(x) = \begin{cases} 200 & \text{if } x = 0 \ 200 + 8x & \text{if } x = 5 \ 200 + 9x & \text{if } x > 5 \ \end{cases} \]

In Python-like pseudocode, the function could look something like this:

def cost_of_shirts(x):
    setup_charge = 200
    if x == 0:
        return setup_charge
    elif x == 5:
        return setup_charge + 8 * x
    else:
        return setup_charge + 9 * x

This function captures the cost structure for different quantities of T-shirts ordered.

Answer 2

sorry I didn't mean 240 I meant 245

Answer 3

No problem! Let's re-evaluate the data with the updated value.

Given Updated Data:

• Number of shirts: 0, 5, 20, 50
• Cost: $200, $245, $380, $650

Step 1: Determine the Setup Charge

As before, for the order of 0 shirts, the cost is $200. This indicates that the setup charge is likely $200.

Step 2: Determine the Cost per Shirt

We can analyze the cost per shirt for the updated cost:

1. For 5 Shirts: \[ \text{Cost} = 245 \] \[ \text{Cost Without Setup Charge} = 245 - 200 = 45 \quad \text{(for 5 shirts)} \] \[ \text{Cost per shirt} = \frac{45}{5} = 9 \]

2. For 20 Shirts: \[ \text{Cost} = 380 \] \[ \text{Cost Without Setup Charge} = 380 - 200 = 180 \quad \text{(for 20 shirts)} \] \[ \text{Cost per shirt} = \frac{180}{20} = 9 \]

3. For 50 Shirts: \[ \text{Cost} = 650 \] \[ \text{Cost Without Setup Charge} = 650 - 200 = 450 \quad \text{(for 50 shirts)} \] \[ \text{Cost per shirt} = \frac{450}{50} = 9 \]

Conclusion:

• Setup Charge: $200
• Cost per Shirt: $9 for orders starting from 5 shirts and above.

Step 3: Write a Function

The function representing the cost can now be defined as follows:

\[ C(x) = \begin{cases} 200 & \text{if } x = 0 \ 200 + 9x & \text{if } x \geq 5 \ \end{cases} \]

In Python-like pseudocode, it would look like this:

def cost_of_shirts(x):
    setup_charge = 200
    if x == 0:
        return setup_charge
    elif x >= 5:
        return setup_charge + 9 * x

This function captures the cost structure for different quantities of T-shirts ordered based on the updated information.