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?
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?
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 when overtime will be needed, we need to calculate the total hours required to produce each unit after the first, using the learning rate.
For the second unit, the time required will be 0.9*2,000 = 1,800 hours.
For the third unit, the time required will be 0.9*1,800 = 1,620 hours.
For the fourth unit, the time required will be 0.9*1,620 = 1,458 hours.
For the fifth unit, the time required will be 0.9*1,458 = 1,312.2 hours, which we'll round up to 1,313 for simplicity.

To calculate the total hours required each month, we need to multiply the number of units produced by the number of hours each unit takes to produce.

Month 1:
- First unit: 2,000 hours
- Total hours: 2,000
- Regular time available: 40 workers * 200 hours = 8,000 hours
- No overtime needed.

Month 2:
- Second unit: 1,800 hours
- Total hours: 3,800
- Regular time available: 8,000 hours
- No overtime needed.

Month 3:
- Third unit: 1,620 hours
- Total hours: 5,420
- Regular time available: 8,000 hours
- Overtime needed: 5,420 - 8,000 = 2,580 hours / 1.5 = 1,720 overtime hours needed.
- Overtime needed for this month only.

Month 4:
- Fourth unit: 1,458 hours
- Total hours: 6,878
- Regular time available: 8,000 hours
- Overtime needed: 6,878 - 8,000 = 1,122 hours / 1.5 = 748 overtime hours needed.
- Overtime needed for this month only.

Month 5:
- Fifth unit: 1,313 hours
- Total hours: 8,191
- Regular time available: 8,000 hours
- Overtime needed: 191 hours / 1.5 = 127 overtime hours needed.
- No regular overtime needed, but some overtime will be needed to finish the last unit.

Therefore, the answer is B: months 3 and 4 only.

The Production for a New Product Follows