Question

The cost of manufacturing bowls at a factory can be modeled by the function below, where C(x) is the total cost, V is the variable cost (the expense of making one bowl), x is the number of bowls made, and R is the cost of renting factory space. If R is $800 for renting the factory space, it costs $2 to make one bowl, and the total cost $2300, how many bowls were made?C (x) = V x + R

Answer 1

We have the function cost:

$C(x)=V\cdot x+R$

The renting cost R is $800.

The variable cost V is $2 per unit.

The total cost is $2300.

We can calculate the number of units x as:

$\begin{gathered} C(x)=V\cdot x+R \\ 2300=2\cdot x+800 \\ 2300-800=2x \\ 1500=2x \\ x=\frac{1500}{2} \\ x=750 \end{gathered}$

Answer: the number of units is 750 (x=750).