'A cleaning company uses $10 of chemicals, $40 of labor, and $5 of misc. expenses for each house it

4 answers
Question:

"A cleaning company uses $10 of chemicals, $40 of labor, and $5 of misc. expenses for each house it cleans. After some quality complaints, the company has decided to increase its use of chemicals by 50%. By what percentage has multifactor productivity fallen?

Answers

multifactor productivity = 8.3%

Explanation:

given data

Total cost for chemicals = $10

Total cost of labor = $40

Total cost of misc = $5

use of chemical = 50%

solution

first we get here total initial cost that is

total initial cost  = 10 + 40 + 5

total initial cost = $55

and

Increase in cost of chemical is = 10 + (0.5) × (10)  

Increase in cost of chemical = 15

so Total increase in cost will be

Total increase in cost = $15 + $40 + $5

Total increase in cost = 60

so

increase in cost % = [tex]\frac{initial\ cost}{incresed\ cost}[/tex]  × 100

increase in cost % = [tex]\frac{55}{60}[/tex]  × 100  

increase in cost % = 91.67 %

so

change in multifactor productivity is  = 100% - 91.7%

multifactor productivity = 8.3%

%age of multifactor productivity reduction = 8.33%

Step-by-step explanation:

Total cost for chemicals = $10

Total cost of labor = $40

Total cost of misc = $5

Total initial cost = 10+40+5 = $55

Increase in use of chemical = 50%

Increase in cost of chemical = 10+ (0.5)(10)  =15

[Note (0.5)(10) is 50% of initial chemical cost]

Total increase in cost= $15+ $40 + $5 =%60

[tex]\%age\,\, of\,\, increase\,\, in \,\,cost =\frac{initial\,\, cost}{incresed\,\,cost}\times 100\%\\\\=\frac{55}{60}\times 100\%\\\\\\= 91.67\%[/tex]

%age of multifactor productivity reduction = 100 - 91.67 = 8.33%

8.3%

Explanation:

initial cost per house = $10 + $40 + $5 = $55 per house

after the 50% increase in the use of chemicals = $15 + $40 + $5 = $60 per house

new multifactor productivity = new cost of 1 clean house / old cost of one clean house = $55 / $60 = 0.917 or 91.7%

so the change in multifactor productivity = 100% - 91.7% = 8.3%

B) 8.3%

Explanation:

The multifactor productivity is given the ratio between output (amount charged per each house cleaned) and input (chemical, labor and misc. expenses)

Let x be the amount charged per housed cleaned, the original and new productivities are:

[tex]P_{old}=\frac{x}{10+40+5}=0.018182x \\P_{new}=\frac{x}{1.5*10+40+5}=0.016667x[/tex]

The rate by which the multifactor productivity has fallen is:

[tex]R = \frac{P_{new}-P_{old}}{P_{old}}\\R=\frac{0.0166667-0.018182}{0.018182} \\R=-0.083=-8.3\%[/tex]

The multifactor productivity has fallen by 8.3%.

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