The demand for Ballard's Glass Company's products varies, ranging from 10 to 20 windows a day with an average of 15. John Ballard works eight hours a day, five days a week. Each order is one window, and each window takes 26 minutes to install. The company plans to add doors to its product line and anticipates selling an average of 5 doors per day. Each door takes 12 minutes to install. What is the average waiting time if Ballard is the only worker?
A) 38.0 minutes
B) 112.4 minutes
C) 181.0 minutes
D) 410.0 minutes
E) 523.4 minutes

Question

Quizplus · Accepted Answer

First, we need to calculate the average installation time for windows:

Daily working hours = 8 hours/day
Total weekly working hours = 5 days/week x 8 hours/day = 40 hours/week

Number of windows installed per week = 15 windows/day x 5 days/week = 75 windows/week

Total installation time for 75 windows = 75 windows x 26 minutes/window = 1950 minutes/week

Average installation time per window = 1950 minutes/week ÷ 75 windows/week = 26 minutes/window

Now, we can calculate the average waiting time for both windows and doors:

Average waiting time for windows = (10 windows/day + 20 windows/day) ÷ 2 x 26 minutes/window = 390 minutes/day

Average waiting time for doors = 5 doors/day x 12 minutes/door = 60 minutes/day

Total average waiting time = Average waiting time for windows + Average waiting time for doors = 450 minutes/day

Finally, we need to account for the fact that John Ballard only works 40 hours/week while the total average waiting time is based on an 8 hour/day operation, so the total average waiting time needs to be divided by 5/8:

Total average waiting time per day = 450 minutes/day x 8/5 = 720 minutes/day

Average waiting time per order = Total average waiting time per day ÷ (15 windows/day + 5 doors/day) = 720 minutes/day ÷ 20 orders/day ≈ 36 minutes/order

Therefore, the average waiting time if Ballard is the only worker is approximately 36 minutes per order, which is closest to option C: 181.0 minutes.

The Demand for Ballard's Glass Company's Products Varies, Ranging from 10