a pizza shop sells pizzas that are 14 inches in diameter or 18 inches in diameter. both pizzas cost $16.50…

planation:

Step1: Identify the fixed - cost and variable - cost components

The fixed cost is the setup cost which is $30$. The variable cost per unit is the cost per piece which is $1.55$. Let $x$ be the number of pieces. The cost function $C(x)$ is the sum of the fixed cost and the variable cost. The variable cost for $x$ pieces is $1.55x$. So, $C(x)=30 + 1.55x$.

Step2: Analyze the given options

We need to find the function that represents the cost $C$ in terms of the number of pieces $x$. Option A: $C(x)=30x+1.55$ is incorrect because the setup cost is a one - time fixed amount and should not be multiplied by $x$. Option B: $C(x)=1.55x + 30$ is correct as it follows the form of the cost function $C(x)=$ fixed cost+variable cost where the fixed cost is $30$ and the variable cost per unit is $1.55$ and for $x$ units, the variable cost is $1.55x$. Option C: $C(x)=30(x + 1.55)$ is incorrect as it distributes the $30$ in an incorrect way for this cost - structure problem. Option D: $C(x)=1.55(x + 30)$ is also incorrect as it does not represent the sum of a fixed and a variable cost in the correct manner.

Answer:

B. $C(x)=1.55x + 30$