A factory produces beach umbrellas. They have a fixed cost they must pay no matter how many umbrellas they produce, and a variable cost they must pay for each umbrella they produce. The cost of producing x

Question

umbrellas is modeled by the function C(x)=2.83x+1,350
. Identify and interpret the initial value.(1 point)
Responses

The initial value of 1,350 represents the fixed cost.
The initial value of 1,350 represents the fixed cost.

The initial value of 2.83 represents the variable cost.
The initial value of 2.83 represents the variable cost.

The initial value of 2.83 represents the fixed cost.
The initial value of 2.83 represents the fixed cost.

The initial value of 1,350 represents the variable cost.

Answer 1

The correct interpretation is:

The initial value of 1,350 represents the fixed cost.

In the cost function \( C(x) = 2.83x + 1,350 \), the fixed cost is the amount that must be paid regardless of the number of umbrellas produced, which is represented by the constant term 1,350. The variable cost is represented by the coefficient of \( x \), which in this case is 2.83, indicating the cost incurred for each additional umbrella produced.