Question

The function C(x)=−21x+3600 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $39?

Answer 1

Step 1

If the average cost of the items produced = 39

Then,

The cost to produce the items should not be more than 39x

Therefore,

$\begin{gathered} \text{The given function is} \\ C(x)\text{ = -21x + 3600} \\ \text{Since the cost to produce the items should not be more than 39x, then} \\ -21x\text{ + 3600}\leq\text{ 39x} \end{gathered}$

Step 2

Simplify and get the final answer

$\begin{gathered} -21x-39x\leq-3600 \\ -60x\leq-3600 \\ \frac{-60x}{-60}\leq\frac{-3600}{-60} \\ x\ge60 \end{gathered}$

Therefore the least number of items that can be produced so that the average cost is no more than $39 = 60 items