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,
[tex]\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}[/tex]
Step 2
Simplify and get the final answer
[tex]\begin{gathered} -21x-39x\leq-3600 \\ -60x\leq-3600 \\ \frac{-60x}{-60}\leq\frac{-3600}{-60} \\ x\ge60 \end{gathered}[/tex]
Therefore the least number of items that can be produced so that the average cost is no more than $39 = 60 items
