3. The manufacturing process at Lone Star Company (LSC) is following a 70% learn

Question

3. The manufacturing process at Lone Star Company (LSC) is following a 70% learning curve. More recently, the company produced four conveyors with the last one requiring 490 labor hours to complete (i.e., P4 = 490). LSC 2 has received an invitation to bid on an order of two additional conveyors. Based on the tables at the end of Chapter 11, what is the total amount of time required to make the fifth and the sixth conveyors?

[Hint: Try to find A first by recalling that each time the output level doubles (from 1 unit to 2 units, from 2 units to 4 units, etc.), the number of labor hours required to complete a task decreases to a fixed percentage of its previous time requirement.]  

( please write clearly all the solutions so I can understand where all numbers came from ) Thank you

Explanation / Answer

Base don the data given, from the learning curve formula, we can find out the time taken to produce the first conveyor.

once we know the time taken for 1st conveyor, based on the same formula, we can find out the time taken for 6th Conveyor. the difference between the cumulative time taken for 6th and 4th conveyor gives the total time taken for 5th and 6th conveyor

learning Curve Equation Tn =T1 *n^b

Tn =nth product

T1 = 1st product

n= number of units

b = log(learning percentage)/log 2

b = log 0.7 / log 2

= -0.15490195999 / 0.301

= -0.515

490 = T1 *4 ^(-0.515)

T1= 490/[4*(-0.515)] = 1000.5 hours

T4 = 490. Hence cumulative labour hours for 1st 4 conveyors = 490 *4 = 1960 hours ------- (x)

Calculate T6

T6 = 1000.5*6^(-0.515)

= 397.6 hours

Cumulative labour hours for 6 conveyors = T6 * 6 = 397.6 * 6 = 2385.7 hours ------- (y)

labour hours fro 5tha nd 6th Conveyor = y-x

=2385.7 - 1960 = 425.72 hours

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