# Please answer the following question about productivity. Deborah packages three flavours of diabetic fudge to sell at nursing homes to help pay for her college fees. She is currently working a...

Deborah packages three flavours of diabetic fudge to sell at nursing homes to help pay for her college fees. She is currently working a total of 4 hours per day to produce 120 packages. What is Deborah’s productivity? Deborah redesigns the package she can work 3 hours per day, produce 140 packages, and dedicate more time to school. What will be her new productivity? What % increase in productivity did Deborah accomplish?

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

In the first part of your question, Deborah is working alone.  We are told only of the time that she puts in working.  That means her labor is the only input that we have to consider when we are calculating her productivity.  Productivity is defined as the amount of output per unit of input.  Since we have only one unit of output (packages of fudge) and one unit of input (hours Deborah works), this is simple.  We divided the output (120 packages) by the input (4 hours).

P = 120 packages/4 hours = 30 packages per hour.

After the redesign, we still use the same equation, only with different numbers.  We divide the 140 packages by 3 hours of labor.

P = 140 packages/3 hours = 46.67 packages per hour.

Now we have to find the percentage increase in her productivity.  To do this, we take the increase in productivity and divide it by the original level of productivity.  To find the increase, we subtract her old productivity from her new.

Change in productivity = 46.67 – 30 = 16.67 packages per hour.

To convert that to a percentage, we divide the change by the original value.

% change = 16.67/30 = .55 or 55%

So, we can see that Deborah achieved a tremendous increase in productivity of 55%.

Sources:
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}