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

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

Answer 1

The cost function is given as \( C(x) = 2.83x + 1,350 \).

In this context:

• The term \( 2.83x \) represents the variable cost, which is the cost incurred for each umbrella produced. The coefficient \( 2.83 \) is the cost per umbrella.
• The term \( 1,350 \) represents the fixed cost, which is the cost that must be paid regardless of how many umbrellas are produced.

Therefore, the initial value of the cost function, when \( x = 0 \) (i.e., no umbrellas are produced), is the fixed cost, which is \( 1,350 \).

Thus, the correct interpretation of the initial value is:

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