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 a umbrellas is

Question

modeled by the function C (x) = 2.83x + 1, 350. Identify and interpret the
initial value. (1 point)
• The initial value of 1,350 represents the fixed cost.
• The initial value of 1,350 represents the variable cost.
• The initial value of 2.83 represents the variable cost.
• The initial value of 2.83 represents the fixed cost.

Answer 1

The correct interpretation of the initial value in the cost function \( C(x) = 2.83x + 1,350 \) is:

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

In this cost function, the fixed cost is the amount that must be paid regardless of the number of umbrellas produced, which is represented by the constant term \( 1,350 \). The term \( 2.83x \) represents the variable cost, which depends on the number of umbrellas produced (x).