College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
14th Edition
ISBN: 9780134674148
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker
Publisher: PEARSON
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 14.1, Problem 1MP
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To find: The functional value C(20,10) of the given cost function.

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Chapter 14 Solutions

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 14.1 - Matched Problem 1 Find C(20, 10) for the cost...Ch. 14.1 - Prob. 2MPCh. 14.1 - Prob. 3MPCh. 14.1 - Prob. 4MPCh. 14.1 - Prob. 5MPCh. 14.1 - Prob. 6MPCh. 14.1 - Prob. 7MPCh. 14.1 - Prob. 1EDCh. 14.1 - Prob. 1ECh. 14.1 - Prob. 2E
Ch. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - Prob. 10ECh. 14.1 - In Problems 9–16, find the indicated values of the...Ch. 14.1 - Prob. 12ECh. 14.1 - In Problems 9–16, find the indicated values of the...Ch. 14.1 - Prob. 14ECh. 14.1 - In Problems 9–16, find the indicated values of the...Ch. 14.1 - Prob. 16ECh. 14.1 - Prob. 17ECh. 14.1 - Prob. 18ECh. 14.1 - In Problems 17–20, find the indicated values...Ch. 14.1 - In Problems 17–20, find the indicated values...Ch. 14.1 - Prob. 21ECh. 14.1 - Prob. 22ECh. 14.1 - In Problems 21–30, find the indicated value of the...Ch. 14.1 - Prob. 24ECh. 14.1 - Prob. 25ECh. 14.1 - Prob. 26ECh. 14.1 - In Problems 21–30, find the indicated value of the...Ch. 14.1 - Prob. 28ECh. 14.1 - Prob. 29ECh. 14.1 - Prob. 30ECh. 14.1 - In Problems 31–36, find the indicated function f...Ch. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Prob. 34ECh. 14.1 - In Problems 31–36, find the indicated function f...Ch. 14.1 - Prob. 36ECh. 14.1 - Prob. 37ECh. 14.1 - Prob. 38ECh. 14.1 - 39. Find a formula for the function C(n, w) of two...Ch. 14.1 - 40. Find a formula for the function N(p, r) of two...Ch. 14.1 - Prob. 41ECh. 14.1 - Prob. 42ECh. 14.1 - Prob. 43ECh. 14.1 - Prob. 44ECh. 14.1 - Prob. 45ECh. 14.1 - Prob. 46ECh. 14.1 - 47. Let F(x, y) = 2x + 3y − 6. Find all values of...Ch. 14.1 - 48. Let F(x, y) = 5x − 4y + 12. Find all values of...Ch. 14.1 - 49. Let F(x, y) = 2xy + 3x − 4y − 1. Find all...Ch. 14.1 - 50. Let F(x, y) = xy + 2x2 + y2 − 25. Find all...Ch. 14.1 - Prob. 51ECh. 14.1 - Prob. 52ECh. 14.1 - Prob. 53ECh. 14.1 - Prob. 54ECh. 14.1 - Prob. 55ECh. 14.1 - Prob. 56ECh. 14.1 - Prob. 57ECh. 14.1 - Prob. 58ECh. 14.1 - Prob. 59ECh. 14.1 - Prob. 60ECh. 14.1 - Prob. 61ECh. 14.1 - Prob. 62ECh. 14.1 - Prob. 63ECh. 14.1 - Prob. 64ECh. 14.1 - 65. Cost function. A small manufacturing company...Ch. 14.1 - Prob. 66ECh. 14.1 - 67. Revenue function. A supermarket sells two...Ch. 14.1 - 68. Revenue, cost, and profit functions. A company...Ch. 14.1 - Prob. 69ECh. 14.1 - Prob. 70ECh. 14.1 - Prob. 71ECh. 14.1 - 72. Package design. The packaging department in a...Ch. 14.1 - Prob. 73ECh. 14.1 - Prob. 74ECh. 14.1 - Prob. 75ECh. 14.1 - Prob. 76ECh. 14.1 - Prob. 77ECh. 14.1 - Prob. 78ECh. 14.2 - Prob. 1MPCh. 14.2 - Prob. 2MPCh. 14.2 - Prob. 3MPCh. 14.2 - Prob. 4MPCh. 14.2 - Prob. 5MPCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - In Problems 1–16, find the indicated derivative....Ch. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Prob. 10ECh. 14.2 - Prob. 11ECh. 14.2 - Prob. 12ECh. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - In Problems 17–24, find the indicated first-order...Ch. 14.2 - In Problems 17–24, find the indicated first-order...Ch. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - In Problems 17–24, find the indicated first-order...Ch. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - In Problems 25–32, find the indicated value. 25. Ch. 14.2 - In Problems 25–32, find the indicated value. 26. Ch. 14.2 - Prob. 27ECh. 14.2 - In Problems 25–32, find the indicated value. 28. Ch. 14.2 - In Problems 25–32, find the indicated value. 29. Ch. 14.2 - Prob. 30ECh. 14.2 - In Problems 25–32, find the indicated value. 31. Ch. 14.2 - Prob. 32ECh. 14.2 - In Problems 33–38, M(x, y) = 68 + 0.3x − 0.8y...Ch. 14.2 - In Problems 33–38, M(x, y) = 68 + 0.3x − 0.8y...Ch. 14.2 - In Problems 33–38, M(x, y) = 68 + 0.3x − 0.8y...Ch. 14.2 - In Problems 33–38, M(x, y) = 68 + 0.3x − 0.8y...Ch. 14.2 - In Problems 33−38, M(x, y) = 68 + 0.3x − 0.8y...Ch. 14.2 - Prob. 38ECh. 14.2 - In Problems 39–50, find the indicated second-order...Ch. 14.2 - Prob. 40ECh. 14.2 - In Problems 39–50, find the indicated second-order...Ch. 14.2 - In Problems 39–50, find the indicated second-order...Ch. 14.2 - In Problems 39–50, find the indicated second-order...Ch. 14.2 - Prob. 44ECh. 14.2 - In Problems 39–50, find the indicated second-order...Ch. 14.2 - Prob. 46ECh. 14.2 - In Problems 39–50, find the indicated second-order...Ch. 14.2 - Prob. 48ECh. 14.2 - In Problems 39–50, find the indicated second-order...Ch. 14.2 - Prob. 50ECh. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - ln Problems 51–60, find the indicated function or...Ch. 14.2 - In Problems 61–66, S(T, r) = 50(T − 40)(5 − r)...Ch. 14.2 - Prob. 62ECh. 14.2 - In Problems 61–66, S(T, r) = 50(T − 40)(5 − r)...Ch. 14.2 - Prob. 64ECh. 14.2 - Prob. 65ECh. 14.2 - Prob. 66ECh. 14.2 - Prob. 67ECh. 14.2 - Prob. 68ECh. 14.2 - In Problems 69–74, find fxx(x, y), fxy(x, y),...Ch. 14.2 - In Problems 69–74, find fxx(x, y), fxy(x, y),...Ch. 14.2 - In Problems 69–74, find fxx(x, y), fxy(x, y),...Ch. 14.2 - In Problems 69–74, find fxx(x, y), fxy(x, y),...Ch. 14.2 - In Problems 69–74, find fxx(x, y), fxy(x, y),...Ch. 14.2 - Prob. 74ECh. 14.2 - Prob. 75ECh. 14.2 - Prob. 76ECh. 14.2 - Prob. 77ECh. 14.2 - Prob. 78ECh. 14.2 - Prob. 79ECh. 14.2 - Prob. 80ECh. 14.2 - Prob. 81ECh. 14.2 - 82. Let f(x, y) = ex + 2ey + 3xy2 + 1. Use...Ch. 14.2 - Prob. 83ECh. 14.2 - Prob. 84ECh. 14.2 - Prob. 85ECh. 14.2 - 86. Advertising and sales. A company spends $x per...Ch. 14.2 - Prob. 87ECh. 14.2 - 88. Revenue and profit functions. A company...Ch. 14.2 - Prob. 89ECh. 14.2 - Prob. 90ECh. 14.2 - Problems 91–94 refer to the following: If a...Ch. 14.2 - Problems 91–94 refer to the following: If a...Ch. 14.2 - Problems 91–94 refer to the following: If a...Ch. 14.2 - Prob. 94ECh. 14.2 - Prob. 95ECh. 14.2 - Prob. 96ECh. 14.2 - Prob. 97ECh. 14.2 - Prob. 98ECh. 14.3 - Prob. 1MPCh. 14.3 - Prob. 2MPCh. 14.3 - Prob. 3MPCh. 14.3 - Prob. 4MPCh. 14.3 - Prob. 1EDCh. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Prob. 3ECh. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14.3 - A In Problems 9–16, find fx(x, y) and fy(x, y),...Ch. 14.3 - Prob. 10ECh. 14.3 - Prob. 11ECh. 14.3 - Prob. 12ECh. 14.3 - A In Problems 9–16, find fx(x, y) and fy(x, y),...Ch. 14.3 - Prob. 14ECh. 14.3 - A In Problems 9–16, find fx(x, y) and fy(x, y),...Ch. 14.3 - Prob. 16ECh. 14.3 - B In Problems 17–36, use Theorem 2 to find the...Ch. 14.3 - Prob. 18ECh. 14.3 - B In Problems 17–36, use Theorem 2 to find the...Ch. 14.3 - Prob. 20ECh. 14.3 - Prob. 21ECh. 14.3 - Prob. 22ECh. 14.3 - Prob. 23ECh. 14.3 - Prob. 24ECh. 14.3 - Prob. 25ECh. 14.3 - Prob. 26ECh. 14.3 - Prob. 27ECh. 14.3 - Prob. 28ECh. 14.3 - B In Problems 17–36, use Theorem 2 to find the...Ch. 14.3 - B In Problems 17–36, use Theorem 2 to find the...Ch. 14.3 - Prob. 31ECh. 14.3 - Prob. 32ECh. 14.3 - B In Problems 17–36, use Theorem 2 to find the...Ch. 14.3 - B In Problems 17–36, use Theorem 2 to find the...Ch. 14.3 - Prob. 35ECh. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Prob. 38ECh. 14.3 - Prob. 39ECh. 14.3 - Prob. 40ECh. 14.3 - Prob. 41ECh. 14.3 - Prob. 42ECh. 14.3 - Prob. 43ECh. 14.3 - 44. Maximizing profit. A store sells two brands of...Ch. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - 47. Minimum material. A rectangular box with no...Ch. 14.3 - 48. Minimum material. A rectangular box with no...Ch. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.4 - Matched Problem 1 Maximize f(x, y) = 25 − x2 – y2...Ch. 14.4 - Prob. 2MPCh. 14.4 - Matched Problem 3 A box of the same type as in...Ch. 14.4 - Prob. 1EDCh. 14.4 - Prob. 2EDCh. 14.4 - Prob. 1ECh. 14.4 - Prob. 2ECh. 14.4 - Prob. 3ECh. 14.4 - In Problems 1–6, maximize or minimize subject to...Ch. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Use the method of Lagrange multipliers in Problems...Ch. 14.4 - Use the method of Lagrange multipliers in Problems...Ch. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Use the method of Lagrange multipliers in Problems...Ch. 14.4 - Prob. 14ECh. 14.4 - Use the method of Lagrange multipliers in Problems...Ch. 14.4 - Prob. 16ECh. 14.4 - Use the method of Lagrange multipliers in Problems...Ch. 14.4 - Prob. 18ECh. 14.4 - Use the method of Lagrange multipliers in Problems...Ch. 14.4 - Use the method of Lagrange multipliers in Problems...Ch. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Use the method of Lagrange multipliers in Problems...Ch. 14.4 - Prob. 25ECh. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - Prob. 29ECh. 14.4 - Prob. 30ECh. 14.4 - 31. Budgeting for least cost. A manufacturing...Ch. 14.4 - 32. Budgeting for maximum production. A...Ch. 14.4 - 33. Productivity. A consulting firm for a...Ch. 14.4 - Prob. 34ECh. 14.4 - 35. Maximum volume. A rectangular box with no top...Ch. 14.4 - Prob. 36ECh. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.5 - Prob. 1MPCh. 14.5 - Prob. 2MPCh. 14.5 - Prob. 1EDCh. 14.5 - Prob. 2EDCh. 14.5 - Prob. 1ECh. 14.5 - Prob. 2ECh. 14.5 - Prob. 3ECh. 14.5 - Prob. 4ECh. 14.5 - Prob. 5ECh. 14.5 - Prob. 6ECh. 14.5 - Prob. 7ECh. 14.5 - Prob. 8ECh. 14.5 - Prob. 9ECh. 14.5 - Prob. 10ECh. 14.5 - Prob. 11ECh. 14.5 - Prob. 12ECh. 14.5 - Prob. 13ECh. 14.5 - Prob. 14ECh. 14.5 - Prob. 15ECh. 14.5 - Prob. 16ECh. 14.5 - Prob. 17ECh. 14.5 - Prob. 18ECh. 14.5 - Prob. 19ECh. 14.5 - Prob. 20ECh. 14.5 - Prob. 21ECh. 14.5 - Prob. 22ECh. 14.5 - Prob. 23ECh. 14.5 - Prob. 24ECh. 14.5 - Prob. 25ECh. 14.5 - Prob. 26ECh. 14.5 - 27. (A) Find the linear and quadratic functions...Ch. 14.5 - Prob. 28ECh. 14.5 - Prob. 29ECh. 14.5 - Prob. 30ECh. 14.5 - Prob. 31ECh. 14.5 - Prob. 32ECh. 14.5 - Prob. 33ECh. 14.5 - Prob. 34ECh. 14.5 - Prob. 35ECh. 14.5 - Prob. 36ECh. 14.5 - Prob. 37ECh. 14.5 - Prob. 38ECh. 14.6 - Prob. 1MPCh. 14.6 - Prob. 2MPCh. 14.6 - Prob. 3MPCh. 14.6 - Prob. 4MPCh. 14.6 - Prob. 5MPCh. 14.6 - Prob. 6MPCh. 14.6 - Prob. 7MPCh. 14.6 - Prob. 1EDCh. 14.6 - Prob. 1ECh. 14.6 - Prob. 2ECh. 14.6 - Prob. 3ECh. 14.6 - Prob. 4ECh. 14.6 - Prob. 5ECh. 14.6 - Prob. 6ECh. 14.6 - Prob. 7ECh. 14.6 - Prob. 8ECh. 14.6 - Prob. 9ECh. 14.6 - Prob. 10ECh. 14.6 - Prob. 11ECh. 14.6 - Prob. 12ECh. 14.6 - Prob. 13ECh. 14.6 - Prob. 14ECh. 14.6 - Prob. 15ECh. 14.6 - Prob. 16ECh. 14.6 - Prob. 17ECh. 14.6 - Prob. 18ECh. 14.6 - Prob. 19ECh. 14.6 - Prob. 20ECh. 14.6 - Prob. 21ECh. 14.6 - Prob. 22ECh. 14.6 - Prob. 23ECh. 14.6 - Prob. 24ECh. 14.6 - Prob. 25ECh. 14.6 - Prob. 26ECh. 14.6 - Prob. 27ECh. 14.6 - Prob. 28ECh. 14.6 - Prob. 29ECh. 14.6 - Prob. 30ECh. 14.6 - Prob. 31ECh. 14.6 - Prob. 32ECh. 14.6 - Prob. 33ECh. 14.6 - Prob. 34ECh. 14.6 - Prob. 35ECh. 14.6 - Prob. 36ECh. 14.6 - Prob. 37ECh. 14.6 - Prob. 38ECh. 14.6 - Prob. 39ECh. 14.6 - Prob. 40ECh. 14.6 - Prob. 41ECh. 14.6 - Prob. 42ECh. 14.6 - Prob. 43ECh. 14.6 - Prob. 44ECh. 14.6 - Prob. 45ECh. 14.6 - Prob. 46ECh. 14.6 - Prob. 47ECh. 14.6 - Prob. 48ECh. 14.6 - Prob. 49ECh. 14.6 - Prob. 50ECh. 14.6 - Prob. 51ECh. 14.6 - Prob. 52ECh. 14.6 - Prob. 53ECh. 14.6 - Prob. 54ECh. 14.6 - Prob. 55ECh. 14.6 - Prob. 56ECh. 14.6 - Prob. 57ECh. 14.6 - Prob. 58ECh. 14.7 - Prob. 1MPCh. 14.7 - Prob. 2MPCh. 14.7 - Prob. 3MPCh. 14.7 - Prob. 4MPCh. 14.7 - Prob. 5MPCh. 14.7 - Prob. 6MPCh. 14.7 - Prob. 7MPCh. 14.7 - Prob. 1EDCh. 14.7 - Prob. 2EDCh. 14.7 - Prob. 1ECh. 14.7 - Prob. 2ECh. 14.7 - Prob. 3ECh. 14.7 - Prob. 4ECh. 14.7 - Prob. 5ECh. 14.7 - Prob. 6ECh. 14.7 - Prob. 7ECh. 14.7 - Prob. 8ECh. 14.7 - Prob. 9ECh. 14.7 - Prob. 10ECh. 14.7 - Prob. 11ECh. 14.7 - Prob. 12ECh. 14.7 - Prob. 13ECh. 14.7 - Prob. 14ECh. 14.7 - Prob. 15ECh. 14.7 - Prob. 16ECh. 14.7 - Prob. 17ECh. 14.7 - Prob. 18ECh. 14.7 - Prob. 19ECh. 14.7 - Prob. 20ECh. 14.7 - Prob. 21ECh. 14.7 - Prob. 22ECh. 14.7 - Prob. 23ECh. 14.7 - Prob. 24ECh. 14.7 - Prob. 25ECh. 14.7 - Prob. 26ECh. 14.7 - Prob. 27ECh. 14.7 - Prob. 28ECh. 14.7 - Prob. 29ECh. 14.7 - Prob. 30ECh. 14.7 - Prob. 31ECh. 14.7 - Prob. 32ECh. 14.7 - Prob. 33ECh. 14.7 - Prob. 34ECh. 14.7 - Prob. 35ECh. 14.7 - Prob. 36ECh. 14.7 - Prob. 37ECh. 14.7 - Prob. 38ECh. 14.7 - Prob. 39ECh. 14.7 - Prob. 40ECh. 14.7 - Prob. 41ECh. 14.7 - Prob. 42ECh. 14.7 - Prob. 43ECh. 14.7 - Prob. 44ECh. 14.7 - Prob. 45ECh. 14.7 - Prob. 46ECh. 14.7 - Prob. 47ECh. 14.7 - Prob. 48ECh. 14.7 - Prob. 49ECh. 14.7 - Prob. 50ECh. 14.7 - Prob. 51ECh. 14.7 - Prob. 52ECh. 14.7 - Prob. 53ECh. 14.7 - Prob. 54ECh. 14.7 - Prob. 55ECh. 14.7 - Prob. 56ECh. 14.7 - Prob. 57ECh. 14.7 - Prob. 58ECh. 14 - Prob. 1RECh. 14 - Prob. 2RECh. 14 - Prob. 3RECh. 14 - Prob. 4RECh. 14 - Prob. 5RECh. 14 - Prob. 6RECh. 14 - Prob. 7RECh. 14 - Prob. 8RECh. 14 - Prob. 9RECh. 14 - Prob. 10RECh. 14 - Prob. 11RECh. 14 - Prob. 12RECh. 14 - Prob. 13RECh. 14 - Prob. 14RECh. 14 - Prob. 15RECh. 14 - Prob. 16RECh. 14 - Prob. 17RECh. 14 - Prob. 18RECh. 14 - 19. Find the average value of f(x, y) = x2/3y2/3...Ch. 14 - Prob. 20RECh. 14 - Prob. 21RECh. 14 - Prob. 22RECh. 14 - Prob. 23RECh. 14 - Prob. 24RECh. 14 - Prob. 25RECh. 14 - Prob. 26RECh. 14 - Prob. 27RECh. 14 - Prob. 28RECh. 14 - Prob. 29RECh. 14 - Prob. 30RECh. 14 - Prob. 31RECh. 14 - Prob. 32RECh. 14 - Prob. 33RECh. 14 - Prob. 34RE
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