Berringer Designs hired a graphic artist.It is estimated that the artist's learning rate is at 70% and her ﬁrst quarter's output amounted to 300 relatively equal job outputs, which took her a total of 50 hours to complete.Output is expected to double in every succeeding quarter. What is the total time requirement as of the 5th quarter? (Do not round your intermediate calculations.)
A)150 hours.
B)175 hours.
C)250 hours.
D)192.08 hours.
E)None of the answers is correct.

Question

Quizplus · Accepted Answer

- The output is expected to double every successive quarter, which means that the output for the 2nd quarter is 600 (300 x 2), the output for the 3rd quarter is 1200 (600 x 2), the output for the 4th quarter is 2400 (1200 x 2), and the output for the 5th quarter is 4800 (2400 x 2).
- According to the learning rate of 70%, the artist's productivity should increase by 70% each quarter. This means that her productivity for the 2nd quarter should be 1.7 times what it was in the 1st quarter, her productivity for the 3rd quarter should be 1.7 times what it was in the 2nd quarter, and so on.
- To calculate the time requirement for each quarter, we need to divide the output by the artist's productivity. For example, for the 1st quarter, her productivity was 300 job outputs / 50 hours = 6 job outputs per hour. For the 2nd quarter, her productivity should be 6 x 1.7 = 10.2 job outputs per hour. Therefore, the time requirement for the 2nd quarter is 600 / 10.2 = 58.8235 hours (do not round).
- Similarly, the time requirements for the 3rd, 4th, and 5th quarters are:

3rd quarter: 1200 / (10.2 x 1.7) = 67.8161 hours
4th quarter: 2400 / (10.2 x 1.7 x 1.7) = 87.6995 hours
5th quarter: 4800 / (10.2 x 1.7 x 1.7 x 1.7) = 192.0803 hours (do not round)

Therefore, the total time requirement as of the 5th quarter is 50 + 58.8235 + 67.8161 + 87.6995 + 192.0803 = 456.4194 hours, which rounded to the nearest whole number is 456 hours.

Berringer Designs Hired a Graphic Artist