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7-14 Fixed cost is $30,000, and...

7-14

Fixed cost is $30,000, and variable cost is $4 per unit. What is the total cost for 20,000 units?

Fixed cost is $30,000, and variable cost is $2 per unit for 10,000 units. If fixed costs increase by 10%, how much will total cost increase?

Total cost is $60,000 to make 20,000 units. Fixed cost is $20,000. What is the variable cost per unit?

We have customers in three locations at grid locations (2,6), (5,1), and (2,2). Each area needs the same quantity. Where is the center of gravity?

We have two customers; one is at coordinates (6,2) and has 200 units of demand, and the other is at (3,4) with 800 units of demand. What is the center of gravity (round to the nearest whole number coordinates)?

7-3

A time study was conducted on a job that contains four elements. The observed times and performance ratings for six cycles are shown in the following table.

OBSERVATIONS (minutes per cycle)

Element Performance

Rating 1 2 3 4 5 6

1 90% 0.44 0.50 0.43 0.45 0.46 0.46

2 85 1.50 1.56 1.47 1.51 1.49 1.52

3 110 0.84 0.89 0.77 0.83 0.83 0.80

4 100 1.10 1.14 1.08 1.20 1.16 1.26

a.

Determine the average cycle time for each element. (Round your answers to 3 decimal places.)

Element Average cycle

1

2

3

4

b.

Find the normal time for each element. (Round your answers to 3 decimal places.)

Element Normal time

1

2

3

4

c.

Assuming an allowance factor of 13 percent of job time, compute the standard time for this job. (Round your answers to 3 decimal places.)

Element Standard time

1

2

3

4

7-2

A job was timed for 60 cycles and had an average of 1.7 minutes per piece. The performance rating was 96 percent, and workday allowances are 16 percent. Determine each of the following:

a. Observed time. (Round your answer to 1 decimal place.)

Observed time minutes

b. Normal time. (Round your answer to 2 decimal places.)

Normal time minutes

c. Standard time. (Round your answer to 2 decimal places.)

Standard time minutes

6-6

Twelve tasks, with times and precedence requirements as shown in the following table, are to be assigned to workstations that have a fixed machine cycle time of 1.5 minutes. Two heuristic rules will be tried: (1) greatest positional weight, and (2) greatest number of following tasks.

In each case, the tiebreaker will be shortest task time.

Task Length

(minutes) Immediate

Predecessor

a 0.1 -

b 0.2 a

c 0.9 b

d 0.6 c

e 0.1 -

f 0.2 d, e

g 0.4 f

h 0.1 g

i 0.2 h

j 0.7 i

k 0.3 j

l 0.2 k

b. Assign tasks to stations under each of the two rules.

(1) greatest positional weight (shortest task time as tiebreaker)

Work Station Tasks

I (Click to select)E, F, G, HA, B, C, DA, BD, E, FA, B, C, E

II (Click to select)D, F, G, H, IH, IJ, K, LD, E, F, HA, B, C, E

III (Click to select)D, F, G, HAA, B, C, EJ, K, LB, D, E

(2) greatest number of following tasks (shortest task time as tiebreaker)

Work Station Tasks

I (Click to select)J, K, LA, B, C, EA, BA, B, C, DD, E, F, G

II (Click to select)A, B, C, EJ, K, LC, D, E, FG, H, ID, F, G, H, I

III (Click to select)E, FC, D, E, FJ, K, LA, B, CD, F, H, I

c.

Compute the percentage of idle time for each rule. (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Percentage of idle time %

6-5

As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of 240 units per eight-hour day. Task times and precedence relationships are as follows:

Task Duration

(minutes) Immediate

Predecessor

a 0.2 -

b 0.4 a

c 0.2 b

d 0.4 -

e 1.2 d

f 1.2 c

g 1.0 e, f

Do each of the following:

b.

Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time. (Round your answers to 1 decimal place.)

The minimum cycle time minutes per unit

The maximum cycle time minutes per unit

Calculated cycle time minutes per unit

c.

Determine the minimum number of stations needed. (Round your answer to the next whole number.)

Minimum number of stations

d.

Assign tasks to workstations on the basis of greatest number of following tasks. Use longest processing time as a tiebreaker. If ties still exist, assume indifference in choice.

Work stations Following Tasks

I (Click to select)AD, B, CA, B, C,DD, C, AA, B, D, C

II (Click to select)AD, C, AEB,EC, F, B

III (Click to select)BFF, GCE

IV (Click to select)GE, FA, B, CEC, D

e.

Compute the percentage of idle time for the assignment in part d. Use the actual bottleneck cycle time in your calculation. (Round your answer to 1 decimal place. Omit the "%" sign in your response.)

Percentage of idle time %

Problem 6-4

A producer of inkjet printers is planning to add a new line of printers, and you have been asked to balance the process, given the following task times and precedence relationships. Assume that cycle time is to be the minimum possible.

Task Length

(minutes) Immediate

Predecessor

a 0.2 -

b 0.4 a

c 0.3 -

d 1.3 b, c

e 0.1 -

f 0.8 e

g 0.3 d, f

h 1.2 g

a. Do each of the following:

(2)

Assign tasks to stations in order of greatest number of following tasks. Use greatest positional weight as a tiebreaker rule.

Work Station Task Assigned

I (Click to select)A, B, C, DD, E, FE, F, G, HA, BA, B, C, E

II (Click to select)ADFBC

III (Click to select)B, DA, EG, HF, GD, C

IV (Click to select)FHADG

Task Following

Tasks

a

b

c

d

e

f

g

h

(3)

Determine the percentage of idle time. (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Percentage of idle time %

(4)

Compute the rate of output in printers per day that could be expected for this line assuming a 420-minute working day. (Round your answer to the nearest whole number.)

Rate of output units per day

b.

Answer these questions:

(1)

What is the shortest cycle time that will permit use of only two workstations? (Round your answer to 1 decimal place.)

Shortest cycle time minutes

(2)

Determine the percentage of idle time that would result if two stations were used and each station was loaded with the worktime shown in Part b(1). (Leave no cells blank - be certain to enter "0" wherever required. Omit the "%" sign in your response.)

Percentage of idle time %

(3)

What is the daily output under this arrangement a using the cycle time from Part b(1)? (Round your answer to 1 decimal place.

Daily output units per day

(4)

Determine the output rate that would be associated with using the maximum cycle time. (Round your answer to 2 decimal places.)

Rate of output units per day

Problem 5-6

A real estate agent is considering changing her cell phone plan. There are three plans to choose from, all of which involve a monthly service charge of $20. Plan A has a cost of $.44 a minute for daytime calls and $.19 a minute for evening calls. Plan B has a charge of $.54 a minute for daytime calls and $.15 a minute for evening calls. Plan C has a flat rate of $80 with 225 minutes of calls allowed per month and a charge of $.40 per minute beyond that, day or evening.

a.

Determine the total charge under each plan for this case: 130 minutes of day calls and 50 minutes of evening calls in a month. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Cost for Plan A $

Cost for Plan B $

Cost for Plan C $

c.

If the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal? (Round each answer to the nearest whole number.Include the indifference point itself in each answer.)

Plan A is optimal from zero to minutes. Plan C is optimal from minutes onward.

d.

Suppose that the agent expects both daytime and evening calls. At what point (i.e., percentage of total call minutes used for daytime calls) would she be indifferent between plans A and B? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places. Omit the "%" sign in your response.)

Point percent daytime minutes

Fixed cost is $30,000, and variable cost is $4 per unit. What is the total cost for 20,000 units?

Fixed cost is $30,000, and variable cost is $2 per unit for 10,000 units. If fixed costs increase by 10%, how much will total cost increase?

Total cost is $60,000 to make 20,000 units. Fixed cost is $20,000. What is the variable cost per unit?

We have customers in three locations at grid locations (2,6), (5,1), and (2,2). Each area needs the same quantity. Where is the center of gravity?

We have two customers; one is at coordinates (6,2) and has 200 units of demand, and the other is at (3,4) with 800 units of demand. What is the center of gravity (round to the nearest whole number coordinates)?

7-3

A time study was conducted on a job that contains four elements. The observed times and performance ratings for six cycles are shown in the following table.

OBSERVATIONS (minutes per cycle)

Element Performance

Rating 1 2 3 4 5 6

1 90% 0.44 0.50 0.43 0.45 0.46 0.46

2 85 1.50 1.56 1.47 1.51 1.49 1.52

3 110 0.84 0.89 0.77 0.83 0.83 0.80

4 100 1.10 1.14 1.08 1.20 1.16 1.26

a.

Determine the average cycle time for each element. (Round your answers to 3 decimal places.)

Element Average cycle

1

2

3

4

b.

Find the normal time for each element. (Round your answers to 3 decimal places.)

Element Normal time

1

2

3

4

c.

Assuming an allowance factor of 13 percent of job time, compute the standard time for this job. (Round your answers to 3 decimal places.)

Element Standard time

1

2

3

4

7-2

A job was timed for 60 cycles and had an average of 1.7 minutes per piece. The performance rating was 96 percent, and workday allowances are 16 percent. Determine each of the following:

a. Observed time. (Round your answer to 1 decimal place.)

Observed time minutes

b. Normal time. (Round your answer to 2 decimal places.)

Normal time minutes

c. Standard time. (Round your answer to 2 decimal places.)

Standard time minutes

6-6

Twelve tasks, with times and precedence requirements as shown in the following table, are to be assigned to workstations that have a fixed machine cycle time of 1.5 minutes. Two heuristic rules will be tried: (1) greatest positional weight, and (2) greatest number of following tasks.

In each case, the tiebreaker will be shortest task time.

Task Length

(minutes) Immediate

Predecessor

a 0.1 -

b 0.2 a

c 0.9 b

d 0.6 c

e 0.1 -

f 0.2 d, e

g 0.4 f

h 0.1 g

i 0.2 h

j 0.7 i

k 0.3 j

l 0.2 k

b. Assign tasks to stations under each of the two rules.

(1) greatest positional weight (shortest task time as tiebreaker)

Work Station Tasks

I (Click to select)E, F, G, HA, B, C, DA, BD, E, FA, B, C, E

II (Click to select)D, F, G, H, IH, IJ, K, LD, E, F, HA, B, C, E

III (Click to select)D, F, G, HAA, B, C, EJ, K, LB, D, E

(2) greatest number of following tasks (shortest task time as tiebreaker)

Work Station Tasks

I (Click to select)J, K, LA, B, C, EA, BA, B, C, DD, E, F, G

II (Click to select)A, B, C, EJ, K, LC, D, E, FG, H, ID, F, G, H, I

III (Click to select)E, FC, D, E, FJ, K, LA, B, CD, F, H, I

c.

Compute the percentage of idle time for each rule. (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Percentage of idle time %

6-5

As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of 240 units per eight-hour day. Task times and precedence relationships are as follows:

Task Duration

(minutes) Immediate

Predecessor

a 0.2 -

b 0.4 a

c 0.2 b

d 0.4 -

e 1.2 d

f 1.2 c

g 1.0 e, f

Do each of the following:

b.

Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time. (Round your answers to 1 decimal place.)

The minimum cycle time minutes per unit

The maximum cycle time minutes per unit

Calculated cycle time minutes per unit

c.

Determine the minimum number of stations needed. (Round your answer to the next whole number.)

Minimum number of stations

d.

Assign tasks to workstations on the basis of greatest number of following tasks. Use longest processing time as a tiebreaker. If ties still exist, assume indifference in choice.

Work stations Following Tasks

I (Click to select)AD, B, CA, B, C,DD, C, AA, B, D, C

II (Click to select)AD, C, AEB,EC, F, B

III (Click to select)BFF, GCE

IV (Click to select)GE, FA, B, CEC, D

e.

Compute the percentage of idle time for the assignment in part d. Use the actual bottleneck cycle time in your calculation. (Round your answer to 1 decimal place. Omit the "%" sign in your response.)

Percentage of idle time %

Problem 6-4

A producer of inkjet printers is planning to add a new line of printers, and you have been asked to balance the process, given the following task times and precedence relationships. Assume that cycle time is to be the minimum possible.

Task Length

(minutes) Immediate

Predecessor

a 0.2 -

b 0.4 a

c 0.3 -

d 1.3 b, c

e 0.1 -

f 0.8 e

g 0.3 d, f

h 1.2 g

a. Do each of the following:

(2)

Assign tasks to stations in order of greatest number of following tasks. Use greatest positional weight as a tiebreaker rule.

Work Station Task Assigned

I (Click to select)A, B, C, DD, E, FE, F, G, HA, BA, B, C, E

II (Click to select)ADFBC

III (Click to select)B, DA, EG, HF, GD, C

IV (Click to select)FHADG

Task Following

Tasks

a

b

c

d

e

f

g

h

(3)

Determine the percentage of idle time. (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Percentage of idle time %

(4)

Compute the rate of output in printers per day that could be expected for this line assuming a 420-minute working day. (Round your answer to the nearest whole number.)

Rate of output units per day

b.

Answer these questions:

(1)

What is the shortest cycle time that will permit use of only two workstations? (Round your answer to 1 decimal place.)

Shortest cycle time minutes

(2)

Determine the percentage of idle time that would result if two stations were used and each station was loaded with the worktime shown in Part b(1). (Leave no cells blank - be certain to enter "0" wherever required. Omit the "%" sign in your response.)

Percentage of idle time %

(3)

What is the daily output under this arrangement a using the cycle time from Part b(1)? (Round your answer to 1 decimal place.

Daily output units per day

(4)

Determine the output rate that would be associated with using the maximum cycle time. (Round your answer to 2 decimal places.)

Rate of output units per day

Problem 5-6

A real estate agent is considering changing her cell phone plan. There are three plans to choose from, all of which involve a monthly service charge of $20. Plan A has a cost of $.44 a minute for daytime calls and $.19 a minute for evening calls. Plan B has a charge of $.54 a minute for daytime calls and $.15 a minute for evening calls. Plan C has a flat rate of $80 with 225 minutes of calls allowed per month and a charge of $.40 per minute beyond that, day or evening.

a.

Determine the total charge under each plan for this case: 130 minutes of day calls and 50 minutes of evening calls in a month. (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Cost for Plan A $

Cost for Plan B $

Cost for Plan C $

c.

If the agent will use the service for daytime calls, over what range of call minutes will each plan be optimal? (Round each answer to the nearest whole number.Include the indifference point itself in each answer.)

Plan A is optimal from zero to minutes. Plan C is optimal from minutes onward.

d.

Suppose that the agent expects both daytime and evening calls. At what point (i.e., percentage of total call minutes used for daytime calls) would she be indifferent between plans A and B? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places. Omit the "%" sign in your response.)

Point percent daytime minutes

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