Final answer:
To determine when it's more advantageous to work for Company B with a lower hourly wage but a signing bonus, we use the inequality $10h + $800 > $11.50h. It shows under what circumstances Company B is the better option, factoring in the signing bonus against the higher hourly rate of Company A.
Step-by-step explanation:
To write an inequality that compares the compensation for employees at Company A and Company B, we need to consider both the hourly wage and any additional bonuses. Company A pays an hourly wage of $11.50, whereas Company B pays a lower hourly wage of $10 but offers an $800 signing bonus.
Let's define 'h' as the number of hours worked. The earnings from Company A can be represented by $11.50h, and the earnings from Company B by $10h + $800.
We want to know when it's more beneficial to work for Company B despite its lower hourly rate, so the inequality will compare the earnings from both companies:
$10h + $800 > $11.50h
This inequality states that as long as the total earnings from Company B (hourly wage plus signing bonus) are greater than the earnings from Company A at the hourly wage, it is more advantageous to work for Company B. This would help one understand under what circumstances (number of hours worked) Company B becomes the better choice despite the lower hourly wage.
In the context of labor economics, if the inequality favors Company B, it can be seen as a strategy to attract employees with a signing bonus in lieu of a higher hourly wage. Labor demand may shift based on the firm's decision to invest in machinery, potentially reducing the number of needed employees, as with the use of three machines at a wage of $24 an hour mentioned in the provided information.