The Mechanical Engineering department of Michigan Technological University has a

Question

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 100 hours. Their improvement (or learning rate) is 0.76, which means that as output is doubled, their time to assemble a car is reduced by 14 %. 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.)

Explanation / Answer

Assuming a proportional decrease in assembly time for output units between doubled quantities, we have

Time required for manufacturing 1st car: Z1 = 100 hours

Time required for manufacturing 2nd car: Z2 = 100x(2)log0.76/log2 = 76 hours

Time required for manufacturing 3rd car: Z3 = 100x(3)log0.76/log2 = 64.73 hours

Total time to manufacture 3 cars = 100+76+64.73 = 240.73 hours

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