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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 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. 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 2.83 represents the variable cost.

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The cost function \( C(x) = 2.83x + 1,350 \) represents the total cost of producing \( x \) umbrellas.

In this function:

  • The term \( 1,350 \) is the constant part of the equation, which represents the fixed cost. This is the cost that must be paid regardless of the number of umbrellas produced.
  • The term \( 2.83x \) represents the variable cost, which is the cost incurred for each additional umbrella produced.

Thus, the correct interpretation of the initial value is:

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