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

Answer 1

The cost function given is \( C(x) = 2.83x + 1,350 \). In this function, the term \( 2.83x \) represents the variable cost, which depends on the number of umbrellas produced (x), and the constant term \( 1,350 \) represents the fixed cost, which is incurred regardless of how many umbrellas are produced.

Thus, the initial value is 1,350, which represents the fixed cost.

So the correct response is: The initial value of 1,350 represents the fixed cost.