Problem $5$

For this problem, labor productivity will be units produced per labor hour. Multifactor productivity will be the revenue from units produced divided by the sum of all costs.

Fifty two weeks of data have been collected on a process, as shown below. The items being produced are sold for $$699$ each.

The cost of material is $$52$ per unit. And labor hours are charged at $$45$ per hour.

Create a column showing labor productivity and then graph it as a function of week.

Also create a column showing multifactor productivity and graph it on a second graph, also as a function of week.

$($That means week is on the $x$ axis, productivity on the $y$ axis. Use a line or dot graph, not a bar or column graph.$)$

Note that in week $27,$ the company implemented some automated technology and transferred two employees to a different product line.

Look at the graphs and answer: what did the implementation of automated equipment do to productivity?

It increased labor productivity greatly and multifactor productivity just a little.Data: Labor Hours Capital Cost Energy Cost Misl. Cost Units Produced Labor productivity Total productivity

$196273002242958693$

$1922730021141106596$

$189273001996959399$

$18727300211610363101$

$18727300211610763104$

$18827300211310591106$

$1882730019999665108$

$18627300194310500110$

$18727300211310357112$

$18527300224210525114$

$1862730024499809115$

$18627300260210830117$

$1852730027669020118$

$18527300260210740120$

$1832730026819018121$

$1832730027639991122$

$18127300303311062123$

$18127300313010586124$

$18227300293910320125$

$1812730032329224126$

$1802730031309516127$

$1812730030349990128$

$18127300285011086129$

$1832730030349103129$

$18127300285310450130$

$18127300303310339131$

$15330010333411041131$

$15030010333510246132$

$1393001035559666132$

$1323001033339481133$

$13630010367210119133$

$13030010344310144134$

$12730010344310024134$

$12230010333310238134$

$12130010333310418135$

$11830010333310608135$

$11530010367010654135$

$11530010367210816136$

$11030010391410443136$

$1103001040469373136$

$11030010417810544136$

$1103001043199006136$

$1093001046139257137$

$1043001043179692137$

$11030010476810417137$

$1043001046109026137$

$10430010476810142137$

$1103001052689137137$

$11030010492910590138$

$1043001047669078138$

$9830010492810552138$

$1103001050969111138$