Karen is a trusted employee whose productivity declines as she works more hours each day. After careful observation of her work performance, her manager prepared the following chart:

| Daily Number of Hours Worked by Karen | Total Number of Work Units Completed |
|---------------------------------------|--------------------------------------|
| 1 | 100 |
| 2 | 190 |
| 3 | 270 |
| 4 | 340 |
| 5 | 400 |
| 6 | 450 |
| 7 | 480 |
| 8 | 500 |

Karen's total cost to the firm is $11 per hour. Each work unit completed is worth $0.21 to the firm.

Ignoring all other possibilities and considerations, for how many hours should the firm hire Karen per day?

Karen's productivity declines after devoting more hours to work per day. Her work performance chart was prepared by her manager. The firm should hire Karen for 5 hours per day based on the given scenario.

Karen's hourly rate is $11. The work performance of Karen is, the value of each work unit completed by Karen is 0.21. The optimal number of hours the firm should hire Karen per day, considering her total cost and the value of each work unit completed.

1. Calculate the profit generated for each number of hours worked: Profit = (Number of work units * $0.21) - (Hours worked * $11)

2. Compare the profit generated for each hour worked to determine the optimal number of hours.

Hours 1: Profit = (100 * $0.21) - (1 * $11) = $21 - $11 = $10

Hours 2: Profit = (190 * $0.21) - (2 * $11) = $39.9 - $22 = $17.9

Hours 3: Profit = (270 * $0.21) - (3 * $11) = $56.7 - $33 = $23.7

Hours 4: Profit = (340 * $0.21) - (4 * $11) = $71.4 - $44 = $27.4

Hours 5: Profit = (400 * $0.21) - (5 * $11) = $84 - $55 = $29

Hours 6: Profit = (450 * $0.21) - (6 * $11) = $94.5 - $66 = $28.5

Hours 7: Profit = (480 * $0.21) - (7 * $11) = $100.8 - $77 = $23.8

Hours 8: Profit = (500 * $0.21) - (8 * $11) = $105 - $88 = $17

The optimal number of hours the firm should hire Karen per day is 5 hours, as it generates the highest profit of $29.

Karen's productivity is the number of work units she completes per hour.

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