A factory produces beach umbrellas. They have 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+1350. Identify and interpret the initial value.
The initial value in this context refers to the fixed cost, which is the cost incurred by the factory regardless of the number of umbrellas produced.
In the given function C(x) = 2.83x + 1350, the constant term 1350 represents the fixed cost.
Interpreting the initial value, it implies that even if the factory does not produce any umbrellas (x = 0), they still have to incur a cost of $1350. This fixed cost covers expenses such as rent, utilities, or salaries, which are necessary for the factory to operate regardless of the level of production.