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1. Exercise 1.1, #61 a. C ( q) =0.01 q 2 + 0.9 q +2 C ( 10 )=0.01 ( 10 ) 2 + 0.9 ( 10 ) +2 C ( 10)=12 b. C ( 10 )C ¿-[ 0.01 ( 9 ) 2 +0.9 ( 9 ) +2 ¿ C ( 10 ) –C( 9 )=1.09 2. Exercise 1.2, #41 cost =15 ∙qtyprice=xqty=5 ( 27x ) =1355 x Let C = cost, R = revenue, P = profit then, C ( x) =15 ( 1355 x)C ( x) =202575x R ( x )=x ( 1355 x )R ( x )=135 x5 x 2 P ( x) =R ( x )C ( x)P ( x) =1355 x 2 −( 202575 x)P ( x) =−5 x 2 +210 x2025 Maximum profit is when P ' ( x ) =0 P ' ( x ) =−10 x+2100=−10 x+21010 x=210x=21 optimal price is $21 per game qty=1355 xqty=1355 (21 ) qty=30 30 sets will be sold each week. 3. Exercise 1.3, #37 Let C=totalcost and x=productioncost per unit . y=C ( x)=60 x +5,000

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1. Exercise 1.1, #61a.

b. -[

2. Exercise 1.2, #41

Let C = cost, R = revenue, P = profit then,

Maximum profit is when optimal price is $21 per game

30 sets will be sold each week.3. Exercise 1.3, #37Let and

4. Exercise 1.3, #46a. NF(N)

1,00050,000

10,000500,000

10,000400,000

20,000800,000

20,000700,000

50,0001,750,000

b.

5. Exercise 1.4, #3a. b. Producing 20,000 units gives a profit of $43,000.

Producing 5,000 units gives a loss of $2,000.

xy

020

3041

7262

10055

6. Exercise 1.4, #32a.

b. Split equally between the 2; use since Profit = 51 thousand dollars

c. Express P in terms of y; * We know that so

7. Exercise 1.4, #42a. Average yield: The total yield:

b.

c.

The grower should grow 80 trees to maximize yield.

8. Exercise 1.4, #52

a.

; 200 tables must be sold to breakeven

b.

; 240 tables must be sold to make a profit of $6,000

c. There will be a loss of $7,500 if 150 tables are sold.

d.

9. Exercise 1.6, #48The graph is discontinuous at and. The company bought more inventories during those months.

10. Exercise 2.1, #50a. b.

The average change in consumer expenditures is -$115 per unit.

c. The instantaneous rate of change is -$80 per unit when . The expenditure is decreasing when .

11. Exercise 2.2, #64Let be the GDP in billions of dollars where is years and represents 1995. Since the GDP is growing at a constant rate, is a linear function passing through the points (0,125) and (8,155).Then Then In 2010, and the model predicts a GDP of billion dollars.

12. Exercise 2.4, #66

13. Exercise 2.5, #1a.

b.

c.

d.

e.

14. Exercise 2.5, #13a. Marginal cost = Derivative of total cost function

b.

$244

15. Exercise 2.5, #24

more worker-hours are needed

16. Exercise 2.6, #55

17. Exercise 3.1, #59a.

b.

207 units will be sold

c.

is the maximum point $11,000 should be spent on advertising to maximize sales2,264 units is the maximum sales level

18. Exercise 3.2, #55a.

1,000 units will be sold

b.

Inflection point when x = 11.

Sales are increasing at the largest rate when $11,000 is spent on marketing.

19. Exercise 3.3, #46a. Vertical Asymptote: x=0To find x-intercept:

Since a square root cannot equal a negative, this equation has no solutions, meaning there is no x-intercept.

To find the y-intercept:

This cannot be done, since it would result in a zero in the denominator, so there is no y-intercept.

Horizontal Asymptote

Since the degree of the numerator (2) exceeds the degree of the denominator (1), there is no horizontal asymptote.

b. The average cost curve C(x) approaches the line as x gets larger.

c.

20. Exercise 3.4, #19a.

P(q) is maximized at q=7

b.

A(q) is minimized at .

21. Exercise 3.4, #27

E(10) < 1 inelastic

22. Exercise 3.4, #47Let h(x) = number of units assembled if the break is taken hours later after 8:00 am

(Minimum)

(Maximum)

=

23. Exercise 3.5, #6Where x is the price

At a price of per book the profit P(x) is maximized at $2,420.

24. Exercise 3.5, #27Let , , , and then,

++(*)

25. Exercise 3.5, #35

5 years from now

26. Exercise 4.1, #39a.

b.

27. Exercise 4.1, #61

28. Exercise 4.2, #47

Let

29. Exercise 4.3, #65a.

Elastic for p > 25; or Inelastic for p < 25; or Of unit elasticity for p = 25; or

b. When , the demand is

The elasticity of demand is Thus, an increase of 1% in price from will result in a decrease in the quantity demanded by approximately 0.6%. Consequently, an increase of 2% in price, from $15 to $15.3, results in a decrease in demand of approximately, from 1,646 to 1,626 units.Demand will decrease by approximately 1.2%c.

30. Exercise 4.3, #73a.

Value is decreasing at the rate of $1,082.69 per year.

b.

Constant rate of 40% per year

31. Exercise 4.4, #25 (graph) (t, y)a. As

b. represent those that will floating at the end of the day 10This is about 74%

c.

About 8.9% will sink from 15th to 20th day.

32. Exercise 4.4, #42a.

b.

The function can be used to evaluate the effectiveness of a training program because as it clearly indicates, by removing the units produced by the new workers who took no special training, we can determine the level of units produced by the average workers after having the special training.The program after 5 weeks as well as after 7 weeks are both effective, because both of them yielded positive results. However, the training program after 5 weeks is more effective for it depicts larger remainder after deducting the units produced by the workers who do not take the program from the ones who took. Hence, that residual amount represents the additional units that a worker can produce after taking the training program.

33. Exercise 5.1, #47

3,253

34. Exercise 5.2, #54Let ,

35. Exercise 5.3, #47

36. Exercise 5.3, #60st week

From 7 to 14 = 2nd week

37. Exercise 5.4, #34

38. Exercise 5.4, #45a.

14.7 yearsb.

$582,221

c.

39. Exercise 5.5, #5a.

b.

40. Exercise 5.5, #13

Producers Surplus

41. Exercise 5.5, #21a. 11 years

b.

Evaluating from to , the profit is $26,620.

c.

42. Exercise 5.5, #29

43. Exercise 5.5, #37a.

b. 9.12 years

c.

$1,218 billion

d. Answers will vary

44. Exercise 5.5, #46

45. Page 466, #68

Total manufacturing cost from 10 13 units.