Question

The stylists in a hair salon cut hair for women and men.

The salon books at least four women's appointments for every man's appointment.
Usually, there are 90 or more appointments, in total, during a week.
The salon is trying to reduce the number of hours the stylists work.
A woman's cut takes about 75 min, and a man's cut takes about 30 min.
What combination of women's and men's appointments would minimize the number of hours the stylists work? How many hours would this be?

A. 20 women's appointments and 5 men's appointments, 195 hours
B. 36 women's appointments and 9 men's appointments, 315 hours
C. 40 women's appointments and 10 men's appointments, 350 hours
D. 48 women's appointments and 12 men's appointments, 420 hours

Answer 1

The combination that minimizes the number of hours worked, while still meeting the requirement of at least 90 appointments per week, is Option B with 36 women's appointments and 9 men's appointments, totaling 49.5 hours.

Step-by-step explanation:

To find the combination of women's and men's appointments that would minimize the number of hours stylists work, we need to calculate the total time for each option provided and choose the least. We know a woman's cut takes 75 minutes (1.25 hours), and a man's cut takes 30 minutes (0.5 hours). Let's calculate the total hours for each option:

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The combination that minimizes the number of hours worked by the stylists is Option A, with a total of 27.5 hours. However, this option does not meet the criteria of at least 90 appointments a week. Therefore, we need to check if any of the other options meet this criterion.

While Option A has the least hours, it only amounts to 25 appointments in total, which is well below the 90 appointment minimum. So, it is invalid. Option B, C, and D all exceed the minimum number of appointments, but Option B has the lowest number of total hours. Thus, the best answer is Option B, with 36 women's appointments and 9 men's appointments, totaling 49.5 hours of work.