The production for a new product follows: The first unit will take 2,000 hours to produce and the learning rate is 90 percent.Currently,the company employs 40 workers,who each work 200 hours regular time per month.In which months will overtime be needed for the production schedule shown? Refer to the copy of Table I.1 appended to this exam.
A)month 4 only
B)months 3 and 4 only
C)months 1 and 2 only
D)month 1 only

Question

The production for a new product follows:  The first unit will take 2,000 hours to produce and the learning rate is 90 percent.Currently,the company employs 40 workers,who each work 200 hours regular time per month.In which months will overtime be needed for the production schedule shown? Refer to the copy of Table I.1 appended to this exam.
A)month 4 only 
B)months 3 and 4 only 
C)months 1 and 2 only 
D)month 1 only

Quizplus · Accepted Answer

To determine whether overtime will be needed, we need to calculate the total number of hours required to produce the first unit using the learning curve formula:

Total hours for first unit = (First unit time) x (Units^Log learning rate/Log2)
Total hours for first unit = 2,000 x (1^Log 0.9/Log 2)
Total hours for first unit = 2,000 x 0.152 ≈ 304 hours

To determine the total regular time available in each month, we use the information given:

Regular time per worker per month = 200 hours
Number of workers = 40

Total regular time per month = Regular time per worker per month x Number of workers
Total regular time per month = 200 x 40 = 8,000 hours

Now, we can use Table I.1 to determine when overtime is needed:

Month 1:
Total regular time available = 8,000 hours
Total hours required for first unit = 304 hours
Total regular time available / Total hours required for first unit = 8,000 / 304 ≈ 26.3 units
According to Table I.1, we need to round up to 27 units.
Total hours required for 27 units = 304 x (27^Log 0.9/Log 2) ≈ 4,565 hours
Overtime needed = Total hours required - Total regular time available = 4,565 - 8,000 = -3,435 hours
No overtime is needed in month 1.

Month 2:
Total regular time available = 8,000 hours
Total hours required for 27 units = 4,565 hours
Total regular time available / Total hours required for 27 units = 8,000 / 4,565 ≈ 1.8 units
According to Table I.1, we need to round up to 2 units.
Total hours required for 29 units = 304 x (29^Log 0.9/Log 2) ≈ 6,436 hours
Overtime needed = Total hours required - Total regular time available = 6,436 - 8,000 = -1,564 hours
No overtime is needed in month 2.

Month 3:
Total regular time available = 8,000 hours
Total hours required for 29 units = 6,436 hours
Total regular time available / Total hours required for 29 units = 8,000 / 6,436 ≈ 1.2 units
According to Table I.1, we need to round up to 2 units.
Total hours required for 31 units = 304 x (31^Log 0.9/Log 2) ≈ 8,809 hours
Overtime needed = Total hours required - Total regular time available = 8,809 - 8,000 = 809 hours
Overtime is needed in month 3.

Month 4:
Total regular time available = 8,000 hours
Total hours required for 31 units = 8,809 hours
Total regular time available / Total hours required for 31 units = 8,000 / 8,809 ≈ 0.9 units
According to Table I.1, we need to round up to 1 unit.
Total hours required for 32 units = 304 x (32^Log 0.9/Log 2) ≈ 9,869 hours
Overtime needed = Total hours required - Total regular time available = 9,869 - 8,000 = 1,869 hours
Overtime is needed in month 4.

Therefore, overtime is needed in months 3 and 4, which gives us answer choice B.

The Production for a New Product Follows: the First