Sample/practice exam 2020, answers PDF

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EXAMPLE 1. If productivity increased from 80 to 84, the growth rate would be Solution: Productivity growth = ((Current Productivity-Previous productivity)/Previous productivity)*100 Productivity growth = ((84-80)/80)*100 = 5% EXAMPLE 2. Determine the productivity for these cases: a. Four workers installed 720 square yards of carpeting in eight hours. b. A machine produced 70 pieces in two hours. However, two pieces were unusable. Solution: a. Productivity = Yards of carpet installed/Labor hours worked = 720 square yards/(4 workers 8 hours/worker) = 720 yards/32 hours = 22.5 yards/hour b. productivity = Usable pieces/Production time = 68 pieces /2 hours [Usable pieces=70-2=68] = 34 pieces /hour. EXAMPLE 3. A company that processes fruits and vegetables is able to produce 400 cases of canned peaches in one-half hour with four workers. What is labor productivity? Solution: Labor productivity = Quantity produced/Labor hours

= 400/(4*0.5) cases per labor hour = 200 cases per labor hour EXAMPLE 4. A wrapping-paper company produced 2,000 rolls of paper one day. Labor cost was $160, material cost was $50, and overhead was $320. Determine the multifactor productivity. Solution: Multifactor productivity = Quantity produced/(Labor cost + Material cost + Overhead) = 2 000 rolls /( $160+ $50+$320) = 3.77 rolls per dollar input A variation of the multifactor productivity calculation incorporates the standard price in the numerator by multiplying the units by the standard price. EXAMPLE 5. Compute the multifactor productivity measure for an eight-hour day in which the usable output was 300 units, produced by three workers who used 600 pounds of materials. Workers have an hourly wage of $20, and material cost is $1 per pound. Overhead is 1.5 times labor cost. Solution: Multifactor productivity = Usable output/(Labor cost+ Material cost+ Overhead cost) Here, Labor cost = (3 workers*8 hours*$20/hour )=$480 Material cost = (600 pounds*$1/pound )=$600 Overhead cost = (3 workers*8 hours*$20/hour*1.5 )=$720 Usable output = 300 units

Multifactor productivity = 300 units/($480+ $600+$720) = 0.167 units of output per dollar of input EXAMPLE 6. A health club has two employees who work on lead generation. Each employee works 40 hours a week, and is paid $20 an hour. Each employee identifies an average of 400 possible leads a week from a list of 8,000 names. Approximately 10 percent of the leads become members and pay a one-time fee of $100. Material costs are $130 per week, and overhead costs are $1,000 per week. Calculate the multifactor productivity for this operation in fees generated per dollar of input. Solution: MFP = (Possible leads)* (No. of workers Fee)*(fee)*(conversion percentage)/ (Labor cost+ Material cost + Overhead cost) = (400*2*$100*0.1)/(2*40*$20)+$130+$1000 = $8000/$2730 = 2.93 PROBLEMS 1. A catering company prepared and served 300 meals at an anniversary celebration last week using eight workers. The week before, six workers prepared and served 240 meals at a wedding reception. a. For which event was the labor productivity higher? Explain. b. What are some possible reasons for the productivity differences? Solution: 1(a.) 300/8= 37.5 & 240/6= 40 The productivity of the first week was higher because they ended up making more meals with fewer workers.

2(b.) Just the overall work ethic of different workers could be possible reason for the difference. Or even the possibility that some were more thoroughly trained versus others. 2. The manager of a crew that installs carpeting has tracked the crew’s output over the past several weeks, obtaining these figures: Week

Crew Size

1 2 3 4 5 6

4 3 4 2 3 2

Yards Installed 96 72 92 50 69 52

a) Compute the labor productivity for each of the weeks. b) On the basis of your calculations, what can you conclude about crew size and productivity? Solution: 2(a.) Productivity = Yards of carpet installed/crew size = 960/4 yards/number of crew. = 240 yards/number of crew.

Week 1 2 3 4 5 6

Crew size 4 3 4 2 3 2

Yards Installed 960 702 968 500 698 500

Labor productivity 240 234 242 250 232.7 250

2(b.) Probably even sized crews are better than odd sizes and a crew of 2 seems to work best amongst the others. 3. a. Compute the multifactor productivity measure for each of the weeks shown for production of chocolate bars. b. What do the productivity figures suggest? Assume 40-hour weeks and an hourly wage of $12. Overhead is 1.5 times weekly labor cost. Material cost is $6 per pound. Week 1 2 3 4

Output (units) 30000 33600 32200 35400

Workers 6 7 7 8

Material (lbs.) 450 470 460 480

Solution: 3(a.) Week 1, worker cost = 12*40*6 =2880 Week 1, overhead cost = 12*40*6 =2880* 1.5=4320 Week 1, material cost = 450*6 = 2700 Week 1, total cost = 2880+4320+2700=9900 Week 1, MFP = output (units)/(labor + materials + overhead) = 30000/9900 = 3.03 unit per dollar input.

Week

Output (units)

Worker cost (12*40)

1 2 3 4

30000 33600 32200 35400

2880 3360 3360 3840

Overhead Materials cost cost

4320 5040 5040 5740

2700 2820 2760 2880

Total cos

MFP

9900 11220 11160 12480

3.03 2.99 2.89 2.84

3(b.) Multi factor productivity dropped steadily from a high of 3.03 to about 2.84.

4. A company that makes shopping carts for supermarkets and other stores recently purchased some new equipment that reduces the labor content of the jobs needed to produce the shopping carts. Prior to buying the new equipment, the company used five workers, who produced an average of 80 carts per hour. Workers receive $10 per hour, and machine cost was $40 per hour. With the new equipment, it was possible to transfer one of the workers to another department, and equipment cost increased by $10 per hour while output increased by four carts per hour. a. Compute labor productivity under each system. Use carts per worker per hour as the measure of labor productivity. b. Compute the multifactor productivity under each system. Use carts per dollar cost (labor plus equipment) as the measure. c. Comment on the changes in productivity according to the two measures, and on which one you believe is the more pertinent for this situation. Solution: 4(a.) Labor Productivity: Before purchase of new equipment: 80/5 = 16 carts per worker per hour. After purchase of new equipment: 84/4 = 21 carts per worker per hour. 4(b.) Multifactor Productivity Before purchase of new equipment: 80/(($10 x 5)+ $40) = 0.89 carts/$1. After purchase of new equipment: 84/(($10 x 4) + $50) = 0.93 carts/$1. 4(c.)

Growth productivity = ((Current Period Productivity – Previous Period Productivity)/Previous Period Productivity)*100 Growth productivity = ((21-16)/16)*100 = 31.25%. Labor productivity increased by 31.25%. Growth productivity = ((Current Period Productivity – Previous Period Productivity)/Previous Period Productivity)*100 Growth productivity = ((0.93-0.89)/0.89)*100 = 4.5%. Multifactor productivity increased by 4.5%. The calculations show that labor productivity is increased after purchase of new equipment, however, multifactor productivity shows that the cost to produce each cart is more expensive with the purchase of new equipment. I believe that the multifactor productivity measure that indicates carts produced per dollar is more pertinent for this situation because it means that there is a lower cost in producing each cart. 5. An operation has a 10 percent scrap rate. As a result, 72 pieces per hour are produced. What is the potential increase in labor productivity that could be achieved by eliminating the scrap? Solution: The 72 pcs/hr. that are produced are NOT scrap, if there is 10% scrap, then 90% * (production + scrap) = 72 pcs/hr. 0.9 * (72+s) = 72 pcs/hr. [Let scrap=s] 72+s = 72/0.8 pcs/hr. 72+s = 80 pcs/hr. s = 80-72 pcs/hr. s = 8 pcs/hr.

Growth productivity = ((Current Period Productivity – Previous Period Productivity)/Previous Period Productivity)*100 Growth productivity = ((80-72)/72)*100 = 11.11%. The increase in production is 11.11%. 6. A manager checked production records and found that a worker produced 160 units while working 40 hours. In the previous week, the same worker produced 138 units while working 36 hours. Did the worker’s productivity increase, decrease, or remain the same? Explain. Solution: Current productivity = produced units as output/ labor hour = 160/40 unit per hour = 4 unit per hour Previous productivity = produced units as output/ labor hour = 138/36 unit per hour = 3.83 unit per hour Growth productivity = ((Current Period Productivity – Previous Period Productivity)/Previous Period Productivity)*100 Growth productivity = ((4-3.83)/3.83)*100 = 4.4 Thus, there was an increase of 4.4% in productivity. 7. The following table shows data on the average number of customers processed by several bank service units each day. The hourly wage rate is $25, the overhead rate is 1.0 times labor cost, and material cost is $5 per customer. Unit Employees Customers Processed/Day A 4 36 B 5 40 C 8 60 D 3 20

a) Compute the labor productivity and the multifactor productivity for each unit. Use an eight-hour day for multifactor productivity.

b) Suppose a new, more standardized procedure is to be introduced that will enable each employee to process one additional customer per day. Compute the expected labor and multifactor productivity rates for each unit. Solution: 7(a.) Uni t

Employee s

A

4

Customer s per Day 36

B

5

40

C

8

60

D

3

20

Labor Cost

Overhead Cost

Material Cost

Total Labor Cost Productivity

MFP

4*8*25=800

800*1=800

5*8*25=100 0 8*8*25=160 0 3*8*25=600

1000*1=100 0 1600*1=160 0 600*1=600

36*5=18 0 40*5=20 0 60*5=30 0 20*5=10 0

178 0 220 0 350 0 130 0

0.02 0 0.01 8 0.01 7 0.01 5

Labor Cost

Overhead Cost

Material Cost

Total Labor Cost Productivity

MFP

4*8*25=800

800*1=800

5*8*25=100 0

1000*1=100 0

36*5=18 0 40*5=20 0

178 0 220 0

0.02 2 0.02 0

36/32=1.12 5 40/40=1 60/64=0.93 8 20/24=0.83 3

MRFA=36/1780=0.020 MRFB=40/2200=0.018 MRFC=60/3500=0.017 MRFD=20/1300=0.015 7(b.) Uni t

Employee s

A

4

Customer s per Day 40

B

5

45

40/32=1.25 45/40=1.12 5

C

8

68

D

3

23

8*8*25=160 0 3*8*25=600

1600*1=160 0 600*1=600

60*5=30 0 20*5=10 0

350 0 130 0

68/64=1.06 3 23/24=0.95 8

MRFA=40/1780=0.022 MRFB=45/2200=0.020 MRFC=68/3500=0.019 MRFD=23/1300=0.018 8. A property title search firm is contemplating using online software to increase its search productivity. Currently an average of 40 minutes is needed to do a title search. The researcher cost is $2 per minute. Clients are charged a fee of $400. Company A’s software would reduce the average search time by 10 minutes, at a cost of $3.50 per search. Company B’s software would reduce the average search time by 12 minutes at a cost of $3.60 per search. Which option would have the highest productivity in terms of revenue per dollar of input? Solution: Productivity of company A = output/( researcher cost + search cost) = 400/ (30*2+3.5) [Reduce hours=40-10=30] = 6.3 revenue/unit per dollar Productivity of company B = output/( researcher cost + search cost) = 400/ (28*2+3.6) [Reduce hours=40-12=28] = 6.7 revenue/unit per dollar From the above mathematical analysis, it can be said that the productivity of Company A is less than that of Company B. That means Company B has higher productivity.

0.01 9 0.01 8

9. A company offers ID theft protection using leads obtained from client banks. Three employees work 40 hours a week on the leads, at a pay rate of $25 per hour per employee. Each employee identifies an average of 3,000 potential leads a week from a list of 5,000. An average of 4 percent actually signs up for the service, paying a one-time fee of $70. Material costs are $1,000 per week, and overhead costs are $9,000 per week. Calculate the multifactor productivity for this operation in fees generated per dollar of input. Solution: There are 3 employees and they find 3,000 potential leads every week, but only 4% actually sign up for that $70 fee. That is: 3(employees)*3,000(leads)*0.04(ratio Effective leads)*$70(fee)=25,200 So, the output or generated fees are 25,200 Our inputs are: Materials are $1,000, Overhead is $9,000 and Labor is 3 employees, working 40 hours at $25 per hour per employee, that is: 3*40*25= $3,000. Total input = $3000+$1000+$9000=$13000

Just the overall work ethic of different workers could be possible reason for the difference. Or even the possibility that some

were more thoroughly trained versus others. We know that, Multifactor Productivity = Output/Total input = 25200/13000 = 1.9385...