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An industrial plant needs to make 100,000 parts per month to meet demand. Each month contains 20 working days, each of which allows for 3 separate 8-hour shifts.

a. If a worker can produce 10 parts/hour, how many workers are needed on each shift?

b. If each shift has 100 workers, what is the productivity of an individual worker?

c. If material costs are $10/part, capital costs are $100,000, and labor costs are $10/hour, what is the multifactor productivity of the plant from part (a)?

Answer :

Answer:

Part A:

Workers Needed=20.833≅21

Part B:

Productivity of individual worker=2.0833 parts/hour

Part C:

Multifactor productivity=0.0832 Parts/$

Explanation:

Part A:

Total parts =100,000

Workers needed= Total parts/(Parts per hour* hours per shift*Total Shifts)

[tex]Worker\ needed=\frac{100000}{10\ Parts/hour*8\ hours/shift*60\ shifts/worker} \\Workers\ needed= 20.833[/tex]

Workers needed=20.833≅21

Part B:

Productivity of individual worker:

[tex]Productivity\ of\ individual\ worker=\frac{100000}{100\ workers*8\ hours/shift*60\ shifts/worker} \\Productivity\ of\ individual\ worker=2.0833\ parts/hour[/tex]

Part C:

Total cost of material= $10*100,000=$1,000,000

Capital Costl= $100,000

Total labor Cost=[tex]21\ workers*8\ hours/shift*60\ shifts/worker*\$10/hour[/tex]

Total labor Cost=$100,800

Multifactor productivity=Total Parts/(Total cost of material+capital cost+Total labor Cost)

[tex]Multifactor\ productivity=\frac{100000}{\$1,000,000+\$100,000+\$100,800} \\ Multifactor\ productivity=0.08324\ Parts/\$[/tex]

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Rewritten by : Barada

Final answer:

The industrial plant needs approximately 21 workers per shift to meet its demand of 100,000 parts per month. An individual worker's productivity, if the shift consists of 100 workers, is 80 parts per worker-hour. The multifactor productivity, considering material, capital, and labor costs, is 0.048 parts per dollar.

Explanation:

In order to answer the questions related to the industrial plant's operations, we'll need to do a few calculations. For question a, we know that there are 20 workdays in a month and that each day consists of 3 shifts of 8 hours each. That is a total of 480 hours in a month. If the plant needs to produce 100,000 parts per month and a worker can produce 10 parts per hour, we'll need 100,000 / 10 = 10,000 worker hours. Thus, since there are 480 hours in a month, the plant would need 10,000 / 480 ≈ 21 workers per shift (rounded up).

For question b, if each shift has 100 workers, and each worker can produce 10 parts per hour for 8 hours, then each worker produces 80 parts in a shift, and the 100 workers together produce 8,000 parts per shift. If we again presume 60 shifts in a month (3 shifts per day for 20 days), then 60 shifts would produce 480,000 parts, which means the productivity of an individual worker is 480,000 parts per month divided by 6,000 worker hours, or 80 parts per worker hour.

Lastly, for question c, multifactor productivity represents the output per unit of combined inputs. The combined costs of material, capital, and labor here are (10 × 100,000) + 100,000 + (10 × 21 workers × 8 hours × 20 days × 3 shifts) = 2,104,000. Therefore, the multifactor productivity is 100,000 parts / 2,104,000 = 0.048 parts per dollar.

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