Question

The managers at Fairfield Engines want to find out the total cost of producing 16 engines. The first unit requires 50 labor-hours and the company expects a learning curve of 80%. The labor cost per hour is $12 and associated overhead costs are $20 per labor hour.
a. Assuming the cumulative average-learning model, what will be the total cost of producing 16 engines?

Answer 1

Answer:

The total cost for conversion considering a learning curve of 80%

will be of $ 14,272 plus materials

Explanation:

cost of the first unit:

50 labor hours x ($20 wages + $12 overhead) = $1,600

As there is a learning curve of 80% the cost will reduce at that rate each time the production doubles

We have to solve this as the sum o the time it takes for each product to be produced:

$\sum_1^n \: \: T_1n^{ln 0.8/ln 2}$

where n is the numebr of unit

units  Tn

1         50

2  40

3  35.10518514

4  32

5  29.78186718

6  28.08414811

7  26.72447623

8  25.6

9  24.64748047

10  23.82549374

11  23.10555693

12  22.46731849

13  21.89577608

14  21.37958099

15  20.90995922

16  20.48

Sum  446.0068426

446 hours labor hours x ($20 wage rat + $12 MO) =

$ 14,272