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

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

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

The initial value of 2.83 represents the fixed cost.

Answer 1

In the cost function \( C(x) = 2.83x + 1,350 \), the initial value is the constant term when \( x = 0 \).

• The term \( 2.83x \) represents the variable cost per umbrella produced (the cost that varies with the number of umbrellas).
• The term \( 1,350 \) represents the fixed costs, which are incurred regardless of the number of umbrellas produced.

Therefore, the correct interpretation of the initial value is:

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