Exercise for Additional Marks

Solar Power is a producer of high-grade solar panels composed of 200 cells. In processing the cells, the company uses 10 solar tabber stringer machines that can produce 100 cells per hour. Currently, the company has 6 technicians per shift, working 3 shifts a day with a 75-minute break. They operate 5 days a week and 4 weeks a month. The man-machine ratio is 1:1.

1. How many panels can they produce in 2 quarters?

2. On day 2, a power failure occurred from 3:05 to 6:25 pm for 1 day. Additionally, from days 2-4, 4 solar tabber machines will be pulled out for maintenance. How many panels will be lost?

3. Find the available panels for a week after considering the loss in part 2.

To calculate the number of panels that can be produced in 2 quarters, we need to consider the production capacity per hour, the number of shifts, and the number of working days.

Number of cells produced per hour:

10 solar tabber stringer machines ˣ 100 cells per hour = 1,000 cells per hour

Number of hours worked per day:

24 hours - 75 minutes break = 23.25 hours

Number of cells produced per day per machine:

1,000 cells per hour ˣ 23.25 hours = 23,250 cells per machine per day

Number of cells produced per day by all machines:

10 machines ˣ 23,250 cells per machine per day = 232,500 cells per day

Number of working days in 2 quarters:

5 working days per week ˣ 4 weeks per month ˣ 2 quarters = 40 working days

Total number of panels produced in 2 quarters:

232,500 cells per day ˣ 40 working days = 9,300,000 cells

Since each panel is composed of 200 cells, we divide the total number of cells by 200 to find the number of panels produced:

9,300,000 cells / 200 = 46,500 panels

On day 2, due to a power failure from 3:05 pm to 6:25 pm, production was halted for 3 hours and 20 minutes. Assuming the machines were not able to produce during this time, the loss can be calculated as follows:

Number of cells lost during power failure:

10 machines ˣ 100 cells per hour ˣ 3.33 hours = 3,330 cells

Number of panels lost during power failure:

3,330 cells / 200 = 16.65 panels (rounded to the nearest whole number)

From days 2 to 4, 4 solar tabber stringer machines will be pulled out for maintenance. Assuming the remaining 6 machines are still operational, the loss can be calculated as follows:

Number of cells lost due to maintenance:

4 machines ˣ 100 cells per hour ˣ 23.25 hours per day ˣ 3 days = 27,600 cells

Number of panels lost due to maintenance:

27,600 cells / 200 = 138 panels

Therefore, the total number of panels lost due to the power failure and maintenance is 16 panels (from the power failure) + 138 panels (from the maintenance) = 154 panels.

To find the available panels for a week after the power failure and maintenance, we subtract the lost panels from the total panels produced in 2 quarters:

Available panels = Total panels - Lost panels

Available panels = 46,500 panels - 138 panels = 46,362 panels

Therefore, the available panels for a week after the power failure and maintenance is 46,346 panels.

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