Question

During the summer, Cassandra’s parents allow her to work to earn some spending money. However, they do not want her to work more than 40 hours a week. She has two jobs lined up—a waitress position, which pays $10 per hour, and an office assistant position, which pays $11 per hour. While the waitress position does not pose a maximum number of hours she can work, the office limits her to, at most, 15 hours a week. Which of the following is true about the hours Cassandra can spend as a waitress (w) and as an office assistant (a) for a given week?

a) The system correctly represents the feasible domain.
b) The critical points (w, a) are (0, 0), (15, 0), (15, 25), and (0, 40).
c) Cassandra can maximize her earnings by working 25 hours as a waitress and 15 hours as an office assistant.
d) It is possible for Cassandra to work 20 hours at each job.

Answer 1

The correct statement regarding Cassandra's work hours is that she can maximize her earnings by working 25 hours as a waitress and 15 hours as an office assistant, given that she must not exceed 40 hours a week in total and can work at most 15 hours as an office assistant.

Step-by-step explanation:

To determine which of the following statements is true regarding the hours Cassandra can work as a waitress ('w') and as an office assistant ('a') within a given week, we need to evaluate her constraints:

• She cannot work more than 40 hours a week in total.
• She can work at most 15 hours a week as an office assistant.

Let's consider each statement:

• The system correctly represents the feasible domain: Not provided, hence we can't verify this statement.
• The critical points (w, a) are (0, 0), (15, 0), (15, 25), and (0, 40): This is incorrect because (15, 25) suggests Cassandra can work a total of 40 hours, exceeding the 15 hour limit for the office job.
• Cassandra can maximize her earnings by working 25 hours as a waitress and 15 hours as an office assistant: This is true, since 25 hours as a waitress and 15 hours as an office assistant equal 40 hours total, the maximum she is allowed to work.
• It is possible for Cassandra to work 20 hours at each job: This is false because working 20 hours as an office assistant exceeds the 15-hour cap for that position.

Therefore, the correct statement about Cassandra's work hours is that she can maximize her earnings by working 25 hours as a waitress and 15 hours as an office assistant.