Cupcakes cost $1.50 each to produce with fixed cost of $50. Express the cost C, of producing the cupcakes as a linear function of x cupcakes produced.
To express the cost C of producing the cupcakes as a linear function of x cupcakes produced, we need to determine the variable cost per cupcake produced and the fixed cost.
Given that cupcakes cost $1.50 each to produce and there is a fixed cost of $50, let's break it down:
The variable cost is the cost that changes in proportion to the number of cupcakes produced. In this case, it is $1.50 per cupcake.
The fixed cost is the cost that remains constant regardless of the number of cupcakes produced. In this case, it is $50.
To express the cost C as a linear function of the number of cupcakes produced (x), we can use the following formula:
C = mx + b
Where:
C is the cost
m is the variable cost per cupcake
x is the number of cupcakes produced
b is the fixed cost
Applying this formula to the given information, we can substitute in the values:
C = ($1.50)x + $50
Therefore, the cost C of producing x cupcakes can be expressed as a linear function:
C = 1.50x + 50.