SOLUTIONS: CHAPTER 2
PRODUCTIVITY FORMULAS:
Productivity = units produced/(workers or machines) * Hours
Multifactor productivity = output/(labor costs + machine costs + material costs + overhead cost)
Problem 1:
(a) 300/8 = 3.75
(b) 240/6 = 4
Productivity is higher when 8 workers are employed
Problem 2:
week crew Yards installed Yards per worker
1 4 960 240
2 3 702 234
3 4 968 242
4 2 500 250
5 3 696 232
6 2 500 250
Most productive when the crew consists of 2 individuals and it appears that even numbered crews are more productive than odd numbered ones.
Problem 3
week output sales material mat. cost labor cost ohead t. cost MFP **
1 300 42,000 45# $270 2880 4320 7470 5.62
2 338 47,320 46# 276 3360 5040 8676 5.45
3 322 45,080 46# 276 3360 5040 8676 5.20
4 354 49,560 48# 286 3840 5760 9888 5.01
** Obtained by dividing the sales by total cost.
PROBLEM 4
Note: Labor productivity is to be based on carts per worker per hour
Original staffing Modified staffing
Number of workers 5 4
Production per hour 80 84
Labor cost per hour $10 $10
Machine cost $40 $50
PART 1:
labor productivity = 80/5 or 16 carts per worker per hour (Original staffing)
= 84.4 or 21 carts per worker per hour (Modified staffing)
PART 2:
Multi-factor productivity is measured in carts per dollar cost of labor and equipment.
Production Labor cost Equipment cost Total cost MFP
original 80 carts $50 $40 $90 80/90 or .89 carts per dollar
modified 84 carts $40 $50 $90 84/90 or .93 carts per dollar
PART 3:
Labor productivity increased by the increase divided by the original production or 5/16 or 31%
The multifactor productivity increased by the increase in multifactor productivity or (.93 - .89)/.89 or 4.5%
PROBLEM 5:
NOTE: The scrap rate = 10%
good product = 72 pieces per hour
good product = .9 * X (where X is the total product
Therefore:
72 = .9X
X = 80 (which is the total product)
10% of 80 = 8 (which is the scrap)
Therefore the maximum possible improvement is based upon all the scrap now being good. That means that all 80 pieces are now good and that there is an increase in good production of 8 units per 8 hours.
therefore the increase in productivity is 8/72 or 8.33%
PROBLEM 6:
Productivity week one is 160/40 or 4 units per hour
Productivity week 2 is 138/36 or 3.83 units per hour
Growth in productivity= (current units productivity - previous periods productivity)/previous periods productivity or
(4 units per hour - 3.83 units per hour)/(3.83 units per hour) = 4.3%
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