A furniture maker has an order for 98 identical tables If th

A furniture maker has an order for 98 identical tables. If the furniture maker estimates his learning curve at 82% and can reach steady production of 7 hours per table on the 6th table, how long should it take to make all the tables? Express your answer in hours to the nearest whole hour.

Solution

Learnig curve is a diagram which is based on the assumption that a person will take highest time to produce first unit of a product. Subsequently he will gain experience when 1st uit is produced. So second unit will take a less time. How much time will be reduced, will depend upon his efficiency level. Suppose first unit has taken 10 hours to complete. His learning curve efeeciency level is 80%. Then for 2nd unit he will take 80% of first units time. It will be 10x80%=8 hours. For third unit, it will be 80% of 2nd unit i.e. 8x80%=6.4 hours. In this manner it will gradually decrease. After a certain quantity produced, it will be almost steady.

Here the person with 82% effeciency has taken 7 hours to maufacture 6th unit. after 6th units his manufacturing time has become steady. So first ascertain time taken for producing first 6 unit. For each previous unit time will be 100/82 times of the time taken for subsequent unit. Thus multiply 7 hours by 100/82 to get time of 5th unit. Similarly multiply 100/82 with 5th unit time to get time for 4th unit and so on. It is shown below:

total production is98 tables. After 6th uit time taken has become steady at 7 hours. So for balance 98-6=92 tables, total time required will be 92x7=644 hours.

Thus for total 98 tables, time required will be-

73+644=717 hours. Answer.