In this question you will derive a simple labour demand curve.

Suppose that the number of calculators a firm can produce per hour (TP) given a certain number of workers (L), is given by: $$TP = 140\ln(L+22)+6 L$$
The cost of using each worker is just their hourly wage (w). So the total labour cost is $C = w L$.

If the price of each calculator is $12, find the profit maximizing wage as a function of number of workers used (L).
$w =$