Question

total costs of two different summer programs as functions of y

Answer 1

To express the total costs of two different summer programs as functions of \( y \), where \( y \) could represent the number of participants, days, or any other relevant variable, we can define two functions as follows:

1. **Program A**:
- Let \( C_A(y) \) be the total cost of Program A.
- Suppose it has a fixed cost (e.g., facility rental, equipment) plus a variable cost (e.g., per participant or per day).
- The cost function can be expressed as:
\[
C_A(y) = F_A + V_A \cdot y
\]
where:
- \( F_A \) is the fixed cost associated with Program A,
- \( V_A \) is the variable cost per participant or per day.

2. **Program B**:
- Let \( C_B(y) \) be the total cost of Program B.
- Similarly, it has a fixed cost and a variable cost.
- The cost function can be expressed as:
\[
C_B(y) = F_B + V_B \cdot y
\]
where:
- \( F_B \) is the fixed cost associated with Program B,
- \( V_B \) is the variable cost per participant or per day.

### Example:

1. **Program A**:
- Fixed cost (\( F_A \)) = $2000,
- Variable cost (\( V_A \)) = $100 per participant.
- Cost Function:
\[
C_A(y) = 2000 + 100y
\]

2. **Program B**:
- Fixed cost (\( F_B \)) = $1500,
- Variable cost (\( V_B \)) = $150 per participant.
- Cost Function:
\[
C_B(y) = 1500 + 150y
\]

### Summary of Total Cost Functions:
- Program A: \( C_A(y) = 2000 + 100y \)
- Program B: \( C_B(y) = 1500 + 150y \)

You can adjust the fixed and variable costs according to the specific details of each program. Calculating the total cost for a given number of participants (or days) can then be done by substituting \( y \) into these equations.