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 answer

The initial value in this context refers to the fixed cost that the factory must pay regardless of the number of umbrellas produced.

In the given function, C(x) = 2.83x + 1,350, the fixed cost (initial value) is 1,350. This means that the factory incurs a cost of $1,350 even if they don't produce any beach umbrellas.

Interpretation: The initial value of $1,350 represents the fixed cost that the factory must bear, including expenses like rent, insurance, administrative costs, etc., which remain constant irrespective of the number of umbrellas produced.