Explain in your own terms what is meant by a \"Point of diminishing returns.\" Relate it to cost,
effort, and return on investment.
Class: Mathematics for Business and Economics
Solution
Diminishing returns means that with the consumption of additional unit of a good, the utility
derived from it decreases. The point od diminishing returns refer to that point from where the
utiltity starts decreasing with the consumption of next unit of the good.
According to this the cost of consuming an additional unit of the good initially falls and then
starts to rise.
Due to dimishing returns, mostly the effort which goes in trying to consume the units after the
point of diminishing returns can be utilized somewhere else to achieve a relatively better good
whereby the point of dimishing returns has not yet reached.
The Return on Investment hence also falls after reaching the point of diminishing returns..
Explain in your own words how to determine if a process is not stati.pdf
1. Explain in your own words how to determine if a process is not statistically stable.
Solution
1. examine the data for a non-normal conditions. Try the box-cox transform or do it
through inspection. If non-normal, transform it and re-assess predictability. 2. If the out of
control is triggered by one or a few points that are dramatically different from the bulk of the
data, take a look to see if there is something different at that time of sampling. if there is a
difference, re-check for predictability without the data used in the limit calculations 3. Look for
multiple distributions/processes. If found, divide the data and assess each part separately. 4.
Begin to average the data over longer and longer time periods. Plot the average data on an i-
chart. you might try it by hour, shift, day week, month, quarter, year…. You will nearly always
find one averageing period that makes the process predictable. That means that there is a
variation cause with a period shorter than the current time period and longer than the last time
period. Now examine your process to see what changes at that rate. You will have found the first
cause to assess in the analyze phase work.
