Mathematical Analysis for Business, Economic and The Life ...

[Pages:6]Mathematical Analysis for Business, Economic and The Life and Social Sciences., Ernest F. Haueussler,Jr., Richard S. Paul., Richard J Wood, Pearson International Edition

Assigment 1 ? Lines, Parabolas and Systems., Problems 3.2

15. Suppose consumers will demand 40 units of a product when the price is $12.75 per unit and 25 unit when the price is $18.75 each. Find the demand equation, assuming that is linear. Find the price per unit when 37 units are demanded.

12.75 40 18.75 12.75 25 40

12.75 40 6 15

15 191.25 6 240

15 6 431.25

0.4 28.75

When 37 units are demanded, the price is

0.437 28.75 14.8 28.75 $13.95

16. The demand per weeks for a CD is 26,000 copies when the price is $12 each and 10,000 copies when the price is $18 each. Find the demand function for the CD, assuming that isi linear

12

26,000

18 12 10,000 26,000

12 26,000 6 16,000

16,000 192,000 6 156,000

16,000 6 348,000

6 16,000 21.75

17. A Refrigator manufacturer will produce 3000 units when the price is $ 940, and 2200 units when the price is $740. Assume the price (Q) and the quantity (Q) produced are linearity related and find the supply function

940

3,000

740 940 2,200 3,000

940 3,000 200 800

800 752,000 200 600,000

800 200 152,000

0.25 190

18. Suppose a manufacturer of shoes will place on the market 50 (thousand pairs) when the price is 35 (dollar per pair) and 35 when the price is 30. Find the supply equation, assuming that price (P) and the quantity (Q) are linearly related.

35 50 30 35 35 50

35 50 5 15

15 525 5 250

15 5 275

1 275 3 15

19. Suppose the cost to produce 10 units of a product is $40 and the cost of 20 units is $70. If cost, C, is linearity related to output, C find a linear eguation relating C dan Q. Find cost to produce 35 unit

40 10 70 40 20 10

40 10 30 10

10 400 30 300

10 30 100

3 10

The cost to produce 35 units is 3 35 10 115

20. An advertiser goes to a printer and is charge $79 for 100 copies of one flyer and $88 for 400 copies of another flyer, This printer charges a fixed setup cost plus a charge for every copy of sinle page flyer. Find a function that describes the cost of a printing job, if x is the number of copies made.

X : the number of copies made TC : total cost

79 100 ........... (1) 88 400 ............ (2)

Equation (1) x 4.........316 4 400

Equation (2)

88 400

228 3

76

Equation (1) 79 100 79 76 100 0.03

The cost of printing job is 76 0.03 x

21. An electric utility company charges residential customers 12.5 cents perkilowatthour plus a base charge each month. One customer's monthly bill comes $ 51.65 for 380 kilowatt. Find a linear function that describes the total monthly charges for electricity if x isi the number of kilowatt-hours used in a month

MC : Mothly Charge ( dollar) BC : Base Charge each month X : the number of kilowatt-hours

12.5 $51.65 12.5 380 $51.65 4,750 $51.65 $47.50 $4.15

The total monthly charges for electricity 4.15 0.125

22. A cancer patient is to receive drug and radiation therapies. Each cubic centimeter of a drug to be used contain 210 curative units and each minute of radiation exposure gives 305 curative units. The patient requires 2410 curative units. If d cubic centimeters of the drug and r minutes of radiation are administered,determine an equation relation d and r. Graphy the equation for d 0 and r 0, the label of horizontal axis as d

210 305 2410

d

r

0

7.9

11.5

0

r-Values

9

8

7

6

5

4

r-Values

3

2

1

0

0

5

10

15

23. Suppose the value of a mountain bike decreases each year by 10% of its original value. If the original value is $ 1,800. Find an equation that expresses the value v of the bike t years after purchase, where 0 10. Sketch the equation, choosing t as the horizontal axis and v as the vertical axis. What is the slope of resulting line.

1,800 180

v= value

2000

1800

1600

1400

1200

1000 800

v= value

600

400

200

0

0

2

4

6

8

10

12

The slope is -180

24. A new television depreciates $ 120 per year, and its worth $340 after four years. Find a function that describes the value of this television, if x is the age of the television in years.

V = value of a television OV = original value

120 For x = 4, 340 120 4 340 480 820

The function of a television after x years is 820 120

25. A new apartment building was sold for $ 960,000 five years after it was purchased . The original owners calculated that the building appreciated $ 45,000 per year while they owned it. Find a linear function that describes the appreciation of the building, if x is the number of years since the original purchase

45,000

For x = 5 960,000 45,000 5 960,000 225,000 735,000

The function of the appreciation of the bulding is 735,000 45,000

26. A house purchased for $ 245,000 is expected tp double in value in 15 years. Find a linear equation that describes the house's value after t years

245,000 For t = 15 490,000 245,000 15 490,000 225,000 265,000 245,000 265,000

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download