Explanation Given: A Tire Town company develops an advertising campaign. The below table gives, the cost per ad package for newspaper and radio, and the number of ads per package. Newspaper Radio Cost per Ad Package ($) 1000 3000 Ads per Package 18 36 The owner wants to spend no more than $18,000 per month and at least 252 ads per month. Definition used: In the region, any point determined by the constraints is called a feasible solution to the line programming problem. Result used: “(i) If a linear programming problem has an optimal solution, then the optimal value of an objective function occurs at corner of the feasible region determined by the constraints. (ii) When a feasible region for a linear programming problem is bounded, the objective function has a maximum and minimum value”. Calculation: Let, the variable x and y represents the number of newspaper ad packages and radio ad packages, respectively. From the given table note that the cost per ad package in newspaper and radio are $1000 and $3000, respectively and the owner can spend for advertising almost $18,000 per month. Here, the word “at most” represents the symbol " ≤ " . Therefore the statement can be written as an inequality, 1000 x + 3000 y ≤ 18 , 000 . Similarly, the ads per package in newspaper and radio are 18 and 36, respectively and the owner wants at least 252 ads per month. Here, the word “at least” represents the symbol " ≥ " . The statement can be written as an inequality, 18 x + 36 y ≥ 252 . Since the number of ads package is positive, the value x ≥ 0 and y ≥ 0 . Therefore, the inequality that describes the cost per ad package and number of ads is, { 1000 x + 3000 y ≤ 18 , 000 18 x + 36 y ≥ 252 x ≥ 0 , y ≥ 0 (1) The boundary equations of the above inequalities are, { 1000 x + 3000 y = 18 , 000 18 x + 36 y = 252 x = 0 , y = 0 (2) Sketch the graph of the straight lines 1000 x + 3000 y = 18 , 000 , 18 x + 36 y = 252 , x = 0 and y = 0 as shown below in Figure 1. From Figure 1, it is observed that the equation (2) divides the plane into 4 parts. The solution region of the given inequality set is obtained as follows. Take any arbitrary test point in the region I, to test the solution region of (1). Let ( 15 , 4 ) be the test point of the region I. Substitute x = 15 and y = 4 in (1) to obtain the system, { 15 , 000 + 12 , 000 ≤ 18 , 000 270 + 144 ≥ 252 15 ≥ 0 , 4 ≥ 0 That is, the simplified inequality is { 27 , 000 ≤ 18 , 000 414 ≥ 252 15 ≥ 0 , 4 ≥ 0 Since the expression 27 , 000 ≤ 18 , 000 is not true, the point ( 15 , 4 ) does not satisfy (1). Thus, the region I is not the solution region of (1). Take any arbitrary test point in the region II, to check the solution region of the equation (1). Let ( 1 , 6 ) be the test point of the region II. Substitute x = 1 and y = 6 in (1) to obtain the system, { 1000 + 18 , 000 ≤ 18 , 000 18 + 216 ≥ 252 1 ≥ 0 , 6 ≥ 0 That is, the simplified inequality is { 19 , 000 ≤ 18 , 000 234 ≥ 252 1 ≥ 0 , 6 ≥ 0 . Since the expressions 19 , 000 ≤ 18 , 000 and 234 ≥ 252 are not true, the point ( 1 , 6 ) does not satisfy (1). Thus, the region II is not a solution region of (1). Take any arbitrary test point in the region III to test the solution region of (1). Let ( 14 , 1 ) be the test point of the region III. Substitute x = 14 and y = 1 in (1) to obtain the system, { 14 , 000 + 3000 ≤ 18 , 000 252 + 36 ≥ 252 14 ≥ 15 , 1 ≥ 4 That is, the simplified inequality is { 17 , 000 ≤ 18 , 000 288 ≥ 252 14 ≥ 15 , 1 ≥ 4

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Chapter 8.2, Problem 24E

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To find: The number of newspaper and packages and radio ad package which maximize the number of people over age 20.

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Chapter 8.2, Problem 23E

Chapter 8.2, Problem 25E

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Chapter 8 Solutions

EBK COLLEGE ALGEBRA IN CONTEXT

Ch. 8.1 - In Exercises 16, graph each inequality. 1. y 5x ...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - In Exercises 710, match each solution of a system...Ch. 8.1 - Prob. 10E

Ch. 8.1 - Prob. 11E Ch. 8.1 - In Exercises 1116, the graph of the boundary...Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - For each system of inequalities in Exercises 1722,...Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - In Exercises 2326, graph the solution of the...Ch. 8.1 - Prob. 25E Ch. 8.1 - In Exercises 2326, graph the solution of the...Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Sales Trix Auto Sales sells used cars. To promote...Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Manufacturing A company manufactures two types of...Ch. 8.1 - Prob. 34E Ch. 8.1 - Production A firm produces three different-size...Ch. 8.1 - Advertising Tire Town is developing an advertising...Ch. 8.1 - Nutrition A privately owned lake contains two...Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Manufacturing Safeco Company produces two types of...Ch. 8.1 - Manufacturing A company manufactures commercial...Ch. 8.1 - Constructing a Box An open box with a square base...Ch. 8.2 - In Exercises 1-4, use the given feasible region...Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Find the maximum possible value of f = 400x + 300y...Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Find the maximum possible value of f = 80x + 160y...Ch. 8.2 - Prob. 12E Ch. 8.2 - Find the minimum possible value of g = 40x + 30y...Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Manufacturing A company manufactures two types of...Ch. 8.2 - Manufacturing Evergreen Company produces two types...Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Politics A political candidate wishes to use a...Ch. 8.2 - Prob. 31E Ch. 8.2 - Manufacturing Kitchen Pride manufactures toasters...Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Find the first 5 terms of the sequence defined by...Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Salaries Suppose you are offered a job with a...Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.3 - Prob. 31E Ch. 8.3 - Prob. 32E Ch. 8.3 - Prob. 33E Ch. 8.3 - Prob. 34E Ch. 8.3 - Prob. 35E Ch. 8.3 - Prob. 36E Ch. 8.3 - Prob. 37E Ch. 8.3 - Prob. 38E Ch. 8.3 - Prob. 39E Ch. 8.3 - Bouncing Ball A ball is dropped from 128 feet. It...Ch. 8.4 - Find the sum of the first 6 terms of the geometric...Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Find the sum of the first 20 terms of the...Ch. 8.4 - Find the sum of the first 15 terms of the...Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - Prob. 10E Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Salaries Suppose you are offered two identical...Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - Prob. 31E Ch. 8.4 - Email Chain Letters Suppose the email chain letter...Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Prob. 36E Ch. 8.4 - Prob. 37E Ch. 8.4 - Prob. 38E Ch. 8.4 - Prob. 39E Ch. 8.4 - Prob. 40E Ch. 8.4 - Prob. 41E Ch. 8.5 - Prob. 1E Ch. 8.5 - Prob. 2E Ch. 8.5 - Prob. 3E Ch. 8.5 - Prob. 4E Ch. 8.5 - Prob. 5E Ch. 8.5 - Prob. 6E Ch. 8.5 - Prob. 7E Ch. 8.5 - Prob. 8E Ch. 8.5 - Prob. 9E Ch. 8.5 - Prob. 10E Ch. 8.5 - Prob. 11E Ch. 8.5 - Prob. 12E Ch. 8.5 - Prob. 13E Ch. 8.5 - Prob. 14E Ch. 8.5 - Prob. 15E Ch. 8.5 - Prob. 16E Ch. 8.5 - Prob. 17E Ch. 8.5 - Prob. 18E Ch. 8.5 - Prob. 19E Ch. 8.5 - Prob. 20E Ch. 8.5 - Prob. 21E Ch. 8.5 - Prob. 22E Ch. 8.5 - Prob. 23E Ch. 8.5 - Prob. 24E Ch. 8.5 - Prob. 25E Ch. 8.5 - Prob. 26E Ch. 8.5 - Prob. 27E Ch. 8.5 - Prob. 28E Ch. 8.5 - Prob. 29E Ch. 8.5 - Prob. 30E Ch. 8.5 - Prob. 31E Ch. 8.5 - Prob. 32E Ch. 8.5 - Prob. 33E Ch. 8.5 - Prob. 34E Ch. 8.5 - Prob. 35E Ch. 8.5 - Prob. 36E Ch. 8.5 - Prob. 37E Ch. 8.5 - Prob. 38E Ch. 8.5 - Prob. 39E Ch. 8.5 - Prob. 40E Ch. 8.5 - Prob. 41E Ch. 8.5 - Prob. 42E Ch. 8.5 - Prob. 43E Ch. 8.5 - Prob. 44E Ch. 8.5 - Prob. 45E Ch. 8.5 - Prob. 46E Ch. 8.5 - Prob. 47E Ch. 8.5 - Prob. 48E Ch. 8.5 - Prob. 49E Ch. 8.5 - Prob. 50E Ch. 8.5 - Prob. 51E Ch. 8.5 - Prob. 52E Ch. 8.5 - Prob. 53E Ch. 8.5 - Prob. 54E Ch. 8.5 - Prob. 55E Ch. 8.5 - Prob. 56E Ch. 8.6 - Prob. 1E Ch. 8.6 - Prob. 2E Ch. 8.6 - Prob. 3E Ch. 8.6 - Prob. 4E Ch. 8.6 - Prob. 5E Ch. 8.6 - Prob. 6E Ch. 8.6 - Prob. 7E Ch. 8.6 - Prob. 8E Ch. 8.6 - Prob. 9E Ch. 8.6 - Prob. 10E Ch. 8.6 - Prob. 11E Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 14E Ch. 8.6 - Prob. 15E Ch. 8.6 - Prob. 16E Ch. 8.6 - Prob. 17E Ch. 8.6 - Prob. 18E Ch. 8.6 - Prob. 19E Ch. 8.6 - Prob. 20E Ch. 8.6 - Prob. 21E Ch. 8.6 - Prob. 22E Ch. 8.6 - Prob. 23E Ch. 8.6 - Expand the following binomial powers. 24. (x y)7 Ch. 8.6 - Prob. 25E Ch. 8.6 - Prob. 26E Ch. 8.6 - Prob. 27E Ch. 8.6 - Prob. 28E Ch. 8.6 - Prob. 29E Ch. 8.6 - Prob. 30E Ch. 8.6 - Prob. 31E Ch. 8.6 - Prob. 32E Ch. 8.6 - Prob. 33E Ch. 8.6 - Prob. 34E Ch. 8.7 - Prob. 1E Ch. 8.7 - Prob. 2E Ch. 8.7 - Prob. 3E Ch. 8.7 - Prob. 4E Ch. 8.7 - Prob. 5E Ch. 8.7 - Prob. 6E Ch. 8.7 - Prob. 7E Ch. 8.7 - Prob. 8E Ch. 8.7 - Prob. 9E Ch. 8.7 - Prob. 10E Ch. 8.7 - Prob. 11E Ch. 8.7 - Prob. 12E Ch. 8.7 - Prob. 13E Ch. 8.7 - Prob. 14E Ch. 8.7 - Prob. 15E Ch. 8.7 - Prob. 16E Ch. 8.7 - Prob. 17E Ch. 8.7 - Prob. 18E Ch. 8.7 - Prob. 19E Ch. 8.7 - Prob. 20E Ch. 8.7 - Prob. 21E Ch. 8.7 - Prob. 22E Ch. 8.7 - Prob. 23E Ch. 8.7 - Prob. 24E Ch. 8.7 - Prob. 25E Ch. 8.7 - Prob. 26E Ch. 8.7 - Prob. 27E Ch. 8.7 - Prob. 28E Ch. 8.7 - Prob. 29E Ch. 8.7 - Prob. 30E Ch. 8.7 - Prob. 31E Ch. 8.7 - Prob. 32E Ch. 8.7 - Prob. 33E Ch. 8.7 - Prob. 34E Ch. 8.7 - Prob. 35E Ch. 8.7 - In Exercises 3336, write the equation of the shape...Ch. 8.7 - Prob. 37E Ch. 8.7 - Prob. 38E Ch. 8.7 - Write the equation of the circle that is tangent...Ch. 8.7 - Prob. 40E Ch. 8.7 - Prob. 41E Ch. 8.7 - Prob. 42E Ch. 8.7 - Prob. 43E Ch. 8.7 - Prob. 44E Ch. 8.7 - Prob. 45E Ch. 8.7 - Prob. 46E Ch. 8.7 - Prob. 47E Ch. 8.7 - Prob. 48E Ch. 8.7 - Prob. 49E Ch. 8.7 - Prob. 50E Ch. 8.7 - Prob. 51E Ch. 8.7 - Prob. 52E Ch. 8.7 - Prob. 53E Ch. 8.7 - Prob. 54E Ch. 8.7 - In Exercises 4160, graph each equation. 55. 4x2 +...Ch. 8.7 - Prob. 56E Ch. 8.7 - Prob. 57E Ch. 8.7 - Prob. 58E Ch. 8.7 - Prob. 59E Ch. 8.7 - Prob. 60E Ch. 8.7 - Bridges A cable of a suspension bridge is...Ch. 8.7 - Prob. 62E Ch. 8.7 - Prob. 63E Ch. 8.7 - Prob. 64E Ch. 8.8 - Prob. 1E Ch. 8.8 - Prob. 2E Ch. 8.8 - Prob. 3E Ch. 8.8 - Prob. 4E Ch. 8.8 - Prob. 5E Ch. 8.8 - Prob. 6E Ch. 8.8 - Prob. 7E Ch. 8.8 - Prob. 8E Ch. 8.8 - Prob. 9E Ch. 8.8 - Prob. 10E Ch. 8.8 - Prob. 11E Ch. 8.8 - Prob. 12E Ch. 8.8 - Prob. 13E Ch. 8.8 - Prob. 14E Ch. 8.8 - Prob. 15E Ch. 8.8 - Prob. 16E Ch. 8.8 - Prob. 17E Ch. 8.8 - Prob. 18E Ch. 8.8 - Prob. 19E Ch. 8.8 - Prob. 20E Ch. 8.8 - Sketch the graph of the ellipse with center at (0,...Ch. 8.8 - Prob. 22E Ch. 8.8 - Prob. 23E Ch. 8.8 - Prob. 24E Ch. 8.8 - Prob. 25E Ch. 8.8 - Prob. 26E Ch. 8.8 - Prob. 27E Ch. 8.8 - Prob. 28E Ch. 8.8 - Prob. 29E Ch. 8.8 - Prob. 30E Ch. 8.8 - Prob. 31E Ch. 8.8 - Prob. 32E Ch. 8.8 - Prob. 33E Ch. 8.8 - Prob. 34E Ch. 8.8 - Prob. 35E Ch. 8.8 - Prob. 36E Ch. 8.8 - Prob. 37E Ch. 8.8 - Prob. 38E Ch. 8.8 - Prob. 39E Ch. 8.8 - Prob. 40E Ch. 8.8 - Prob. 41E Ch. 8.8 - Prob. 42E Ch. 8.8 - Prob. 43E Ch. 8.8 - Prob. 44E Ch. 8.8 - Prob. 45E Ch. 8.8 - Prob. 46E Ch. 8.8 - Prob. 47E Ch. 8.8 - Prob. 48E Ch. 8.8 - Prob. 49E Ch. 8.8 - Prob. 50E Ch. 8.8 - Prob. 51E Ch. 8.8 - Prob. 52E Ch. 8.8 - Prob. 53E Ch. 8.8 - Prob. 54E Ch. 8 - Prob. 1RE Ch. 8 - Prob. 2RE Ch. 8 - Prob. 3RE Ch. 8 - Prob. 4RE Ch. 8 - Prob. 5RE Ch. 8 - Prob. 6RE Ch. 8 - Prob. 7RE Ch. 8 - Prob. 8RE Ch. 8 - Prob. 9RE Ch. 8 - Prob. 10RE Ch. 8 - Prob. 11RE Ch. 8 - Prob. 12RE Ch. 8 - Prob. 13RE Ch. 8 - Prob. 14RE Ch. 8 - Prob. 15RE Ch. 8 - Prob. 16RE Ch. 8 - Prob. 17RE Ch. 8 - Find the sum of the first 12 terms of the sequence...Ch. 8 - Prob. 19RE Ch. 8 - Prob. 20RE Ch. 8 - Prob. 21RE Ch. 8 - Prob. 22RE Ch. 8 - Write f(x) = 8x3 + 5x1 + 4x with no negative...Ch. 8 - Prob. 24RE Ch. 8 - Prob. 25RE Ch. 8 - Prob. 26RE Ch. 8 - Prob. 27RE Ch. 8 - Prob. 28RE Ch. 8 - Prob. 29RE Ch. 8 - Prob. 30RE Ch. 8 - Prob. 31RE Ch. 8 - Prob. 32RE Ch. 8 - Prob. 33RE Ch. 8 - Prob. 34RE Ch. 8 - Prob. 35RE Ch. 8 - Prob. 36RE Ch. 8 - Prob. 37RE Ch. 8 - Prob. 38RE Ch. 8 - Prob. 39RE Ch. 8 - Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Manufacturing Ace Manufacturing produces two types...Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Manufacturing A company manufactures leaf blowers...Ch. 8 - Profits A woman has a building with 60 two-bedroom...Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Bridges The towers of a suspension bridge are 800...Ch. 8 - Prob. 57RE Ch. 8 - Prob. 58RE

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The number of newspaper and packages and radio ad package which maximize the number of people over age 20.

Solution Summary: The author calculates the cost per ad package for newspaper and radio, and the number of ads per package.

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Chapter 8 Solutions