Question

Question

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
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 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.

Answer 1

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

In this function:

• The term \( 2.83x \) represents the variable cost per umbrella produced. Specifically, \( 2.83 \) is the cost associated with producing one additional umbrella.
• The term \( 1,350 \) represents the fixed cost, which is the cost incurred regardless of the number of umbrellas produced.

Thus, the initial value is \( 1,350 \), and it represents the fixed cost.

So the correct interpretation is:

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