Question & Answer

Hugh has the choice between investing in a City of Heflin bond at 6 percent or investing in a Surething Inc. bond at 9 percent.  Assuming that both bonds have the same nontax characteristics and that Hugh has a 40 percent marginal tax rate, in which bond should he invest?

Melinda invests $200,000 in a City of Heflin bond that pays 6 percent interest.  Alternatively, Melinda could have invested the $200,000 in a bond recently issued by Surething Inc. that pays 8 percent interest and has risk and other nontax characteristics similar to the City of Heflin bond.  Assume Melinda’s marginal tax rate is 25 percent.  

Using the facts in problem 40, if Scot and Vidia earn an additional $80,000 of taxable income, what is their marginal tax rate on this income?  How would your answer differ if they, instead, had $80,000 of additional deductions?

Scot and Vidia, married taxpayers, earn $240,000 in taxable income and $5,000 in interest from an investment in City of Tampa bonds.  Using the U.S. tax rate schedule for married filing jointly (see Example 1-3), how much federal tax will they owe?  What is their average tax rate?  What is their effective tax rate?  What is their current marginal tax rate?

Using the facts in problem 38, if Jorge and Anita earn an additional $100,000 of taxable income, what is their marginal tax rate on this income?  What is their marginal rate if, instead, they reported an additional $100,000 in deductions?

Jorge and Anita, married taxpayers, earn $150,000 in taxable income and $40,000 in interest from an investment in City of Heflin bonds.  Using the U.S. tax rate schedule for married filing jointly (see Example 1-3), how much federal tax will they owe?  What is their average tax rate?  What is their effective tax rate?  What is their current marginal tax rate?

Using the facts in problem 36, if Campbell earns an additional $15,000 of taxable income, what is her marginal tax rate on this income?  What is her marginal rate if, instead, she had $15,000 of additional deductions?

Campbell, a single taxpayer, earns $400,000 in taxable income and $2,000 in interest from an investment in State of New York bonds.  Using the U.S. tax rate schedule (see Appendix C), how much federal tax will she owe?  What is her average tax rate?  What is her effective tax rate?  What is her current marginal tax rate?

Using the facts in problem 34, if Chuck earns an additional $40,000 of taxable income, what is his marginal tax rate on this income?  What is his marginal rate if, instead, he had $40,000 of additional deductions?

Chuck, a single taxpayer, earns $75,000 in taxable income and $10,000 in interest from an investment in City of Heflin bonds.  Using the U.S. tax rate schedule (see Appendix C), how much federal tax will he owe?  What is his average tax rate?  What is his effective tax rate?  What is his current marginal tax rate?

A laser triangulation system is used to determine the height of a steel block. The system has a

photosensitive detector that is located 750.000 mm above the working surface and the laser is

mounted at a 30.00° angle from the vertical. With no part on the worktable, the position of the

laser reflection on the photo sensor is recorded. After a part is placed on the worktable, the laser

reflection shifts 70.000 mm toward the laser. Determine the height of the object.

A laser triangulation system has the laser mounted at a 35° angle from the vertical. The distance

between the worktable and the photodetector is 24.0000 in. Determine (a) the distance between

the laser and the photodetector when no part is present and (b) the height of a part when the

distance between the laser and photo-detector is 12.0250 in.

The additional operation in the preceding problem will add $2.00 to the current cost of the part,

which is $13.50. If the rate of returns from the customer at the tolerance of ±0.025 in is 2.1%, and

it is expected to drop to zero returns using the new tolerance, should the company add the finish

grinding operation to the manufacturing sequence for the part? Answer this question using the

basic cost and return rate data without consideration of the Taguchi loss function.

A company produces a certain part whose most important dimension is 37.50 ±0.025 in. If the

tolerance is exceeded, the customer will return the part to the manufacturer at a cost of $200 in

rework and replacement expenses. (a) Determine the constant k in the Taguchi loss function, Eq.

(42.13). (b) The company can add a finish grinding operation that will allow the tolerance to be

reduced to ±0.010 in. Using the loss function from part (a) what is the value of the loss associated

with this new tolerance?

The inspection department in an automobile final assembly plant inspects cars coming off the

production line against 55 quality features considered important to customer satisfaction. The

department counts the number of defects found per 100 cars, which is the same type of metric

used by a national consumer advocate agency. During a one-month period, a total of 16,582 cars

rolled off the assembly line. These cars included a total of 6045 defects of the 55 features, which

translates to 36.5 defects per 100 cars. In addition, a total of 1955 cars had one or more of the

defects during this month. Determine DPMO, DPM, and DUPM in a Six Sigma program for

these data and convert each to its corresponding sigma level.

In the previous problem, if the foundry desired to improve its quality performance to the 5.0

sigma level in all three measures of DPM, how many defects and defective units would they

produce in an annual production quantity of 15,000 castings? Assume the same eight features are

used to assess quality.

A foundry that casts turbine blades inspects for eight features that are considered critical-toquality.

During the previous month, 1,236 castings were produced. During inspection, 47 defects

among the eight features were found, and 29 castings had one or more defects. Determine DPMO,

DPM, and DUPM in a Six Sigma program for these data and convert each to its corresponding

sigma level.

Twelve cars were inspected after final assembly. The number of defects found ranged between 87

and 139 defect per car with an average of 116. Determine the center and upper and lower control

limits for the c chart that might be used in this situation.

The upper and lower control limits for a p chart are: LCL = 0 and UCL = 0.20. Determine the

minimum possible sample size n that is compatible with this control chart.

The upper and lower control limits for a p chart are: LCL = 0.19 and UCL = 0.24. Determine the

sample size n that is used with this control chart.

The yield of good chips during a certain step in silicon processing of integrated circuits averages

91%. The number of chips per wafer is 200. Determine the center, LCL, and UCL for the p chart

that might be used for this process.

Ten samples of equal size are taken to prepare a p chart. The total number of parts in these ten

samples was 900 and the total number of defects counted was 117. Determine the center, LCL and

UCL for the p chart.

A p chart is to be constructed. Six samples of 25 parts each have been collected, and the average

number of defects per sample was 2.75. Determine the center, LCL and UCL for the p chart.

Seven samples of 5 parts each have been collected from an extrusion process that is in statistical

control, and the diameter of the extrudate has been measured for each part. The calculated values of

x for each sample are (inch) 1.002, 0.999, 0.995, 1.004, 0.996, 0.998, and 1.006. The values of R

are (inch) 0.010, 0.011, 0.014, 0.020, 0.008, 0.013, and 0.017, respectively. (a) Determine the

values of the center, LCL, and UCL for x and R charts. (b) Construct the control charts and plot the

sample data on the charts.

Ten samples of size n = 8 have been collected from a process in statistical control, and the

dimension of interest has been measured for each part. The calculated values of x for each sample

are (mm) 9.22, 9.15, 9.20, 9.28, 9.19, 9.12, 9.20, 9.24, 9.17, and 9.23. The values of R are (mm)

0.24, 0.17, 0.30, 0.26, 0.26, 0.19, 0.21, 0.32, 0.21, and 0.23, respectively. (a) Determine the values

of the center, LCL, and UCL for the x and R charts. (b) Construct the control charts and plot the

sample data on the charts.