Calc. Homework Assignment-MGT3

Calc. Homework Assignment-MGT3

8-4

題目 1: (1 分)

Find the equation of the least-squares line for the given data.

Draw a scatter diagram for the given data and graph the least-squares line.

1 3 5 7 9

9 7 6 3 2

(a)

(b)

(c)

(d)

題目 2: (1 分)

The Social Security (FICA) wage base (in thousands of dollars) from to is given in the

following table:

Year, x 1996 1997 1998 1999 2000 2001

Wage Base, y 62.7 65.4 68.4 72.6 76.2 80.4

Find an equation of the least-squares line for these data. (Let represent the year .)

Please round the coefficients in your equation to three decimal places. Use the result to estimate the

FICA wage base in the year .

(a) ,

(b) ,

(c) ,

(d) ,

題目 3: (1 分)

The projections of male life expectancy at age in the United States are summarized in the following

table.

Year, x 0 10 20 30 40 50

Years Beyond 65, y 15.7 16.8 17.6 18.6 19.1 20.1

(Here, corresponds to the beginning of 2000.)

Find the equation of the least-squares line for these data.

Use the equation found to estimate the life expectancy at of a male in 2050.

(a) , years

(b) , years

(c) , years

(d) , years

題目 4: (1 分)


Draw a scatter diagram for the given data and graph the least-squares line.

, , , ,

(a)

(b)

(c)

(d)

題目 5: (1 分)

The following table gives the total sales of drugs (in billions of dollars) in one country from ( )

through :

Year, x 0 1 2 3 4

Sales, y 120 138 163 180 203

Find an equation of the least-square line for these data.

(a)

(b)

(c)

(d)

(e)

題目 6: (1 分)

The management of Kaldor, a manufacturer of electric motors, submitted the following data in the annual

report to its stockholders.

The table shows the net sales (in millions of dollars) during the years that have elapsed since the new

management team took over. (The first year the firm operated under the new management corresponds

to the time period , and the four subsequent years correspond to .)

Year, 1 2 3 4 5

Net Sales , 427 440 464 494 506

Determine the equation of the least-squares line for these data and use it to predict the net sales for the

upcoming year.Determine the equation of the least-squares line for these data and use it to predict the

net sales for the upcoming year.

(a) millions of dollars

(b) millions of dollars

(c) millions of dollars

(d) millions of dollars

(e) millions of dollars

題目 7: (1 分)

Because of new, lower standards, experts in a study conducted in early projected a rise in the

market for cholesterol-reducing drugs.

The any market (in billions of dollars) for such drugs from through is given in the following

table ( represents ):

Year, x 1999 2000 2001 2002 2003 2004

Market, y 11.79 14.24 17.05 19.17 22.08 23.35

Find an equation of the least-squares line for these data.

Please round coefficients to the nearest hundredth if necessary.

Estimate the market for cholesterol-reducing drugs in 2005, assuming the trend continued.

(a) billion

(b) billion

(c) billion

(d) billon

題目 8: (1 分)

The following data, compiled by the admissions office at Faber College during the past 5 years, relate the

number of college brochures and follow-up letters ( ) sent to a preselected list of high school juniors

who had taken the PSAT and the number of completed applications ( ) received from these students

(both measured in units of ).

Year, 1 2 3 4 5

Average Score, 436 438 428 430 426

Determine the equation of the least-squares line for these data. Use the result obtained to predict the

average SAT verbal score of high school seniors years from now ( ). Please round your answer

to the nearest whole number.

(a) ,

(b) ,

(c) ,

(d) ,

題目 9: (1 分)


Please round the coefficients to the nearest hundredth.

1 1 2 3 4 4 5

1.5 4 5 6 7 8.5 9

(a)

(b)

(c)

(d)

(e)

題目 10: (1 分)

With an aging population, the demand for health care, as measured by outpatient visits, is steadily

growing.

The number of outpatient visits (in million) from through is recorded in the following table

( corresponds to ):

Year, x 0 1 2 3 4 5 6 7 8 9 10

Market, y 326 338 360 387 412 438 441 464 489 508 516

Find an equation on the least-squares line for these data.

Please round coefficients to the nearest hundredth if necessary.

(a)

(b)

(c)

(d)

(e)

8-5

題目 11: (1 分)

Maximize the function

subject to the constraint .

(a)

(b)

(c)

(d)

(e)

題目 12: (1 分)

A building in the shape of a rectangular box is to have a volume of cubic feet.

It is estimated that the annual heating and cooling costs will be dollars per square foot for the top,

dollars per square foot for the front and back, and dollars per square foot for the sides.

Find the dimensions of the building that will result in a minimal annual heating and cooling cost.

What is the minimal annual heating and cooling cost(C)?

(a)

(b)

(c)

(d)

題目 13: (1 分)

Minimize the function

subject to the constraint

(a)

(b)

(c)

(d)

題目 14: (1 分)

Find the maximum and minimum values of the function


(a)

Maxima:

Minima:

(b)

Maxima:

Minima:

(c)

Maxima:

Minima:

(d)

Maxima:

Minima:

題目 15: (1 分)

The management of UNICO Department Store decides to enclose an area outside their building

to display potted plants.

The enclosed area will be a rectangle, one side of which is provided by the external walls of the store.

Two sides of the enclosure will be made of pine board, and the fourth side will be made of galvanized

steel fencing material.

If the pine board fencing costs dollars running foot and the steel fencing costs dollars per running

foot, determine the dimensions of the enclosure that will cost the least to erect.

Round your answers to two decimal places.

(a) by

(b) by

(c) by

(d) by

題目 16: (1 分)


subject to the constraint

(a)

(b)

(c)

(d)

題目 17: (1 分)



____________

題目 18: (1 分)

The total weekly profit (in dollars) realized by Country Workshop in manufacturing and selling its rolltop

desks is given by the profit function

where stands for the number of finished units and denotes the number of unfinished units

manufactured and sold each week.

The company's management decides to restrict the manufacture of these desks to a total of exactly

units per week.

How many finished and how many unfinished units should be manufactured each week to maximize the

company's weekly profit?

__________ finished units

__________ unfinished units

題目 19: (1 分)

The total daily profit (in dollars) realized by Weston Publishing in publishing and selling its dictionaries is

given by the profit function

where stands for the number of deluxe editions and denotes the number of standard editions sold

daily.

Weston's management decides that publication of these dictionaries should be restricted to a total of

exactly copies/day.

How many deluxe copies and how many standard copies should be published each day to maximize

Weston's daily profit?

Find the number of deluxe copies. __________

Find the number of standard copies. __________

題目 20: (1 分)

A building in the shape of a rectangular box is to have a volume of cubic feet.

It is estimated that the annual heating and cooling costs will be dollars per square foot for the top,

dollars per square foot for the front and back, and dollars per square foot for the sides.

Find the dimensions of the building that will result in a minimal annual heating and cooling cost.

What is the minimal annual heating and cooling cost(C)?

__________ __________ __________ __________

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Calc. Homework Assignment-MGT3