Question

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 1

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)

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

Workers needed=20.833≅21

Part B:

Productivity of individual worker:

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

Part C:

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

Capital Costl= $100,000

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

Total labor Cost=$100,800

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

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

Answer 2

a. 20.833 workers would be needed for each shift.

b. The productivity of an individual worker would be 2.0833 parts/hour.

c. The multifactor productivity of the plant from part A would be 0.0832 Parts/per dollar.

How to calculate the needed number of workers?

$\frac{100,000}{10*8*60} \\=\frac{100,000}{4800} \\=20.833$

How to calculate the productivity of each worker?

$\frac{100,000}{100*8*60} \\=\frac{100,000}{48000} \\=2.0833$

How to calculate multifactor productivity for part A?

First, we would compute the total cost for material as;

$10*100,000\\=1,000,000$

Now, the total labor cost would be:

$21*8*60*10\\=100800$

Therefore, multifactor productivity would be;

$\frac{100,000}{1000,000*100,000*100800} \\=0.08324$

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