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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? A) 0% B) 8.3% C) 25% D) 50% E) 16.7%

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pedrocarratore

Answer:

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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