Download Mathematical Analysis for Business, Economic and The Life and

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
21.75
16,000
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
800
200
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
275
1
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
0
11.5
r
7.9
0
r-Values
9
8
7
6
5
4
3
2
1
0
r-Values
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
v= value
800
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 "