Question

QUESTION 4 The Mechanical Engineering department of Michigan Technological University has a student team that is designing a formula car for national competition. The time required for the team to assemble the first car is 60 hours. Their improvement (or learning rate) is 0.72, which means that as output is doubled, their time to assemble a car is reduced by 28 %. Use this information to determine the total time (in hours) required to assemble the first 3 cars. (Enter your answer as a number without the units.)

Answer 1

We are given that learning rate is 0.72

Time required to assemble first car=K=60 hours

Time required to assemble second car=Y₂=60*(1-28%)=43.20 hours

(If output is doubled, their assembly time is reduced by 28%)

We need to calculate the time required to assemble 3rd car.

We know that

Y_x=Kxⁿ

Where

Yx is the time required to produce x th unit

x=Unit number=3

b=learning percentage=0.72

n=log₁₀(0.72)/log₁₀(2)=-0.47393

Y_x=Kxⁿ

Y₃=60*3^-0.47393=35.65 hours

Time required to assemble first 3 units=60+43.20+35.65=138.85 hours