Mathematical Applications for the ...

11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

In Problems 23-30, round all calculations to 2 decimal places.

Supply and demand Use the supply and demand schedules in Problems 27 and 28, with p in dollars and x as the number of units.

Supply Schedule Demand Schedule

x p x p

0 120 0 2400

10 260 10 1500

20 380 20 1200

30 450 30 950

40 540 40 800

50 630 50 730

60 680 60 680

70 720 70 640

Production Suppose that the rate of production of a product (in units per week) is measured at the end of each of the first 5 weeks after start-up and the data in the table are obtained.

Weeks t Rate R(t) Weeks t Rate R(t)

0 250.0 3 243.3

1 247.6 4 241.3

2 245.4 5 239.5

Approximate the total number of units produced in the first 5 weeks.

To determine

To calculate: The total number of units produced in the first 5 weeks if the rate of production of a product (in units per week) is measured at the end of each of the first 5 weeks after start-up and the data in the table is obtained:

*Weeks t*	*Rate R(t)*	*Weeks t*	*Rate R(t)*
0	250.0	3	243.3
1	247.6	4	241.3
2	245.4	5	239.5

Explanation

Given Information:

The rate of production of a product (in units per week) is measured at the end of each of the first 5 weeks after start-up and the data in the table are obtained:

*Weeks t*	*Rate R(t)*	*Weeks t*	*Rate R(t)*
0	250.0	3	243.3
1	247.6	4	241.3
2	245.4	5	239.5

Formula Used:

As per the Trapezoidal Rule:

If f is continuous on [a,b], then,

∫abf(x)dx≈h2[f(x0)+2f(x1)+2f(x2)+2f(x3)+…+2f(xn−2)+2f(xn−1)+f(xn)]

Where h=b−an and n is the number of equal subdivisions of [a,b].

Calculation:

The rate of production of a product (in units per week) is measured at the end of each of the first 5 weeks after start-up and the data in the table are obtained:

*Weeks t*	*Rate R(t)*	*Weeks t*	*Rate R(t)*
0	250.0	3	243.3
1	247.6	4	241.3
2	245.4	5	239.5

In order to apply the rule, the value of h is as follows:

h=1

So, the interval [0,5] is divided into 5 subintervals as follows,

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Chapter 13 Solutions

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Sect-13.1 P-1CP Sect-13.1 P-2CP Sect-13.1 P-1E Sect-13.1 P-2E Sect-13.1 P-3E Sect-13.1 P-4E Sect-13.1 P-5E Sect-13.1 P-6E Sect-13.1 P-7E Sect-13.1 P-8E

Sect-13.1 P-9E Sect-13.1 P-10E Sect-13.1 P-11E Sect-13.1 P-12E Sect-13.1 P-13E Sect-13.1 P-14E Sect-13.1 P-15E Sect-13.1 P-16E Sect-13.1 P-17E Sect-13.1 P-18E Sect-13.1 P-19E Sect-13.1 P-20E Sect-13.1 P-21E Sect-13.1 P-22E Sect-13.1 P-23E Sect-13.1 P-24E Sect-13.1 P-25E Sect-13.1 P-26E Sect-13.1 P-27E Sect-13.1 P-28E Sect-13.1 P-29E Sect-13.1 P-30E Sect-13.1 P-31E Sect-13.1 P-32E Sect-13.1 P-33E Sect-13.1 P-34E Sect-13.1 P-35E Sect-13.1 P-36E Sect-13.1 P-37E Sect-13.1 P-38E Sect-13.1 P-39E Sect-13.1 P-40E Sect-13.2 P-1CP Sect-13.2 P-2CP Sect-13.2 P-1E Sect-13.2 P-2E Sect-13.2 P-3E Sect-13.2 P-4E Sect-13.2 P-5E Sect-13.2 P-6E Sect-13.2 P-9E Sect-13.2 P-10E Sect-13.2 P-11E Sect-13.2 P-12E Sect-13.2 P-7E Sect-13.2 P-8E Sect-13.2 P-23E Sect-13.2 P-24E Sect-13.2 P-13E Sect-13.2 P-14E Sect-13.2 P-15E Sect-13.2 P-16E Sect-13.2 P-17E Sect-13.2 P-18E Sect-13.2 P-19E Sect-13.2 P-20E Sect-13.2 P-21E Sect-13.2 P-22E Sect-13.2 P-25E Sect-13.2 P-26E Sect-13.2 P-27E Sect-13.2 P-28E Sect-13.2 P-29E Sect-13.2 P-30E Sect-13.2 P-31E Sect-13.2 P-32E Sect-13.2 P-33E Sect-13.2 P-34E Sect-13.2 P-35E Sect-13.2 P-36E Sect-13.2 P-37E Sect-13.2 P-38E Sect-13.2 P-39E Sect-13.2 P-40E Sect-13.2 P-41E Sect-13.2 P-42E Sect-13.2 P-43E Sect-13.2 P-44E Sect-13.2 P-45E Sect-13.2 P-46E Sect-13.2 P-47E Sect-13.2 P-48E Sect-13.2 P-49E Sect-13.2 P-50E Sect-13.2 P-51E Sect-13.2 P-52E Sect-13.2 P-53E Sect-13.2 P-54E Sect-13.2 P-55E Sect-13.2 P-56E Sect-13.2 P-57E Sect-13.2 P-58E Sect-13.2 P-59E Sect-13.2 P-60E Sect-13.2 P-61E Sect-13.2 P-62E Sect-13.2 P-63E Sect-13.2 P-64E Sect-13.2 P-65E Sect-13.2 P-66E Sect-13.2 P-67E Sect-13.2 P-68E Sect-13.3 P-1CP Sect-13.3 P-2CP Sect-13.3 P-3CP Sect-13.3 P-1E Sect-13.3 P-2E Sect-13.3 P-3E Sect-13.3 P-4E Sect-13.3 P-5E Sect-13.3 P-6E Sect-13.3 P-7E Sect-13.3 P-8E Sect-13.3 P-9E Sect-13.3 P-10E Sect-13.3 P-11E Sect-13.3 P-12E Sect-13.3 P-13E Sect-13.3 P-14E Sect-13.3 P-15E Sect-13.3 P-16E Sect-13.3 P-17E Sect-13.3 P-18E Sect-13.3 P-19E Sect-13.3 P-20E Sect-13.3 P-21E Sect-13.3 P-22E Sect-13.3 P-23E Sect-13.3 P-24E Sect-13.3 P-25E Sect-13.3 P-26E Sect-13.3 P-27E Sect-13.3 P-28E Sect-13.3 P-29E Sect-13.3 P-30E Sect-13.3 P-31E Sect-13.3 P-32E Sect-13.3 P-33E Sect-13.3 P-34E Sect-13.3 P-35E Sect-13.3 P-36E Sect-13.3 P-37E Sect-13.3 P-38E Sect-13.3 P-39E Sect-13.3 P-40E Sect-13.3 P-41E Sect-13.3 P-42E Sect-13.3 P-43E Sect-13.3 P-44E Sect-13.3 P-45E Sect-13.3 P-46E Sect-13.3 P-47E Sect-13.3 P-48E Sect-13.3 P-49E Sect-13.3 P-50E Sect-13.4 P-1CP Sect-13.4 P-2CP Sect-13.4 P-3CP Sect-13.4 P-1E Sect-13.4 P-2E Sect-13.4 P-3E Sect-13.4 P-4E Sect-13.4 P-5E Sect-13.4 P-6E Sect-13.4 P-7E Sect-13.4 P-8E Sect-13.4 P-9E Sect-13.4 P-10E Sect-13.4 P-11E Sect-13.4 P-12E Sect-13.4 P-13E Sect-13.4 P-14E Sect-13.4 P-15E Sect-13.4 P-16E Sect-13.4 P-17E Sect-13.4 P-18E Sect-13.4 P-19E Sect-13.4 P-20E Sect-13.4 P-21E Sect-13.4 P-22E Sect-13.4 P-23E Sect-13.4 P-24E Sect-13.4 P-25E Sect-13.4 P-26E Sect-13.4 P-27E Sect-13.4 P-28E Sect-13.4 P-29E Sect-13.4 P-30E Sect-13.4 P-31E Sect-13.4 P-32E Sect-13.4 P-33E Sect-13.4 P-34E Sect-13.4 P-35E Sect-13.4 P-36E Sect-13.5 P-1CP Sect-13.5 P-2CP Sect-13.5 P-3CP Sect-13.5 P-4CP Sect-13.5 P-5CP Sect-13.5 P-6CP Sect-13.5 P-1E Sect-13.5 P-2E Sect-13.5 P-3E Sect-13.5 P-4E Sect-13.5 P-5E Sect-13.5 P-6E Sect-13.5 P-7E Sect-13.5 P-8E Sect-13.5 P-9E Sect-13.5 P-10E Sect-13.5 P-11E Sect-13.5 P-12E Sect-13.5 P-13E Sect-13.5 P-14E Sect-13.5 P-15E Sect-13.5 P-16E Sect-13.5 P-17E Sect-13.5 P-18E Sect-13.5 P-19E Sect-13.5 P-20E Sect-13.5 P-21E Sect-13.5 P-22E Sect-13.5 P-23E Sect-13.5 P-24E Sect-13.5 P-25E Sect-13.5 P-26E Sect-13.5 P-27E Sect-13.5 P-28E Sect-13.5 P-29E Sect-13.5 P-30E Sect-13.5 P-31E Sect-13.5 P-32E Sect-13.5 P-33E Sect-13.5 P-34E Sect-13.5 P-35E Sect-13.5 P-36E Sect-13.5 P-37E Sect-13.5 P-38E Sect-13.5 P-39E Sect-13.5 P-40E Sect-13.5 P-41E Sect-13.5 P-42E Sect-13.6 P-1CP Sect-13.6 P-2CP Sect-13.6 P-1E Sect-13.6 P-2E Sect-13.6 P-3E Sect-13.6 P-4E Sect-13.6 P-5E Sect-13.6 P-6E Sect-13.6 P-7E Sect-13.6 P-8E Sect-13.6 P-9E Sect-13.6 P-10E Sect-13.6 P-11E Sect-13.6 P-12E Sect-13.6 P-13E Sect-13.6 P-14E Sect-13.6 P-15E Sect-13.6 P-16E Sect-13.6 P-17E Sect-13.6 P-18E Sect-13.6 P-19E Sect-13.6 P-20E Sect-13.6 P-21E Sect-13.6 P-22E Sect-13.6 P-23E Sect-13.6 P-24E Sect-13.6 P-25E Sect-13.6 P-26E Sect-13.6 P-27E Sect-13.6 P-28E Sect-13.6 P-29E Sect-13.6 P-30E Sect-13.6 P-31E Sect-13.6 P-32E Sect-13.6 P-33E Sect-13.6 P-34E Sect-13.6 P-35E Sect-13.6 P-36E Sect-13.6 P-37E Sect-13.6 P-38E Sect-13.7 P-1CP Sect-13.7 P-2CP Sect-13.7 P-1E Sect-13.7 P-2E Sect-13.7 P-3E Sect-13.7 P-4E Sect-13.7 P-5E Sect-13.7 P-6E Sect-13.7 P-7E Sect-13.7 P-8E Sect-13.7 P-9E Sect-13.7 P-10E Sect-13.7 P-11E Sect-13.7 P-12E Sect-13.7 P-13E Sect-13.7 P-14E Sect-13.7 P-15E Sect-13.7 P-16E Sect-13.7 P-17E Sect-13.7 P-18E Sect-13.7 P-19E Sect-13.7 P-20E Sect-13.7 P-21E Sect-13.7 P-22E Sect-13.7 P-23E Sect-13.7 P-24E Sect-13.7 P-25E Sect-13.7 P-26E Sect-13.7 P-27E Sect-13.7 P-28E Sect-13.7 P-29E Sect-13.7 P-30E Sect-13.7 P-31E Sect-13.7 P-32E Sect-13.7 P-33E Sect-13.7 P-34E Sect-13.7 P-35E Sect-13.7 P-36E Sect-13.7 P-37E Sect-13.7 P-38E Sect-13.7 P-39E Sect-13.7 P-40E Sect-13.7 P-41E Sect-13.7 P-42E Sect-13.7 P-43E Sect-13.7 P-44E Sect-13.7 P-45E Sect-13.7 P-47E Sect-13.8 P-1CP Sect-13.8 P-2CP Sect-13.8 P-3CP Sect-13.8 P-1E Sect-13.8 P-2E Sect-13.8 P-3E Sect-13.8 P-4E Sect-13.8 P-5E Sect-13.8 P-6E Sect-13.8 P-7E Sect-13.8 P-8E Sect-13.8 P-9E Sect-13.8 P-10E Sect-13.8 P-11E Sect-13.8 P-12E Sect-13.8 P-13E Sect-13.8 P-14E Sect-13.8 P-15E Sect-13.8 P-16E Sect-13.8 P-17E Sect-13.8 P-18E Sect-13.8 P-19E Sect-13.8 P-20E Sect-13.8 P-21E Sect-13.8 P-22E Sect-13.8 P-23E Sect-13.8 P-24E Sect-13.8 P-25E Sect-13.8 P-26E Sect-13.8 P-27E Sect-13.8 P-28E Sect-13.8 P-29E Sect-13.8 P-30E Sect-13.8 P-31E Sect-13.8 P-32E Sect-13.8 P-33E Sect-13.8 P-34E Ch-13 P-1RE Ch-13 P-2RE Ch-13 P-3RE Ch-13 P-4RE Ch-13 P-5RE Ch-13 P-6RE Ch-13 P-7RE Ch-13 P-8RE Ch-13 P-9RE Ch-13 P-10RE Ch-13 P-11RE Ch-13 P-12RE Ch-13 P-13RE Ch-13 P-14RE Ch-13 P-15RE Ch-13 P-16RE Ch-13 P-17RE Ch-13 P-18RE Ch-13 P-19RE Ch-13 P-20RE Ch-13 P-21RE Ch-13 P-22RE Ch-13 P-23RE Ch-13 P-24RE Ch-13 P-25RE Ch-13 P-26RE Ch-13 P-27RE Ch-13 P-28RE Ch-13 P-29RE Ch-13 P-30RE Ch-13 P-31RE Ch-13 P-32RE Ch-13 P-33RE Ch-13 P-34RE Ch-13 P-35RE Ch-13 P-36RE Ch-13 P-37RE Ch-13 P-38RE Ch-13 P-39RE Ch-13 P-40RE Ch-13 P-41RE Ch-13 P-42RE Ch-13 P-43RE Ch-13 P-44RE Ch-13 P-45RE Ch-13 P-46RE Ch-13 P-47RE Ch-13 P-48RE Ch-13 P-49RE Ch-13 P-50RE Ch-13 P-51RE Ch-13 P-53RE Ch-13 P-54RE Ch-13 P-55RE Ch-13 P-1T Ch-13 P-2T Ch-13 P-3T Ch-13 P-4T Ch-13 P-5T Ch-13 P-6T Ch-13 P-7T Ch-13 P-8T Ch-13 P-9T Ch-13 P-10T Ch-13 P-11T Ch-13 P-12T Ch-13 P-13T Ch-13 P-14T Ch-13 P-15T Ch-13 P-16T

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Supply Schedule		Demand Schedule
x	p	x	p
0	120	0	2400
10	260	10	1500
20	380	20	1200
30	450	30	950
40	540	40	800
50	630	50	730
60	680	60	680
70	720	70	640

Weeks t	Rate R(t)	Weeks t	Rate R(t)
0	250.0	3	243.3
1	247.6	4	241.3
2	245.4	5	239.5

MathMathematical Applications for the Management, Life, and Social Sciences11th Edition

Mathematical Applications for the ...

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Mathematical Applications for the ...

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Chapter 13 Solutions

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Mathematical Applications for the Management, Life, and Social Sciences 11th Edition