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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Chapter 14.6, Problem 1ED
(A)
To determine
To guess: The function which gives the greater average value by comparing with the given functions.
(B)
To determine
To check: The function has greater value using the double integral.
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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. 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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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- Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 34.4 27.1 30.8 28.0 32.2 27.6 32.8 25.2 31.4 33.5 24.7 28.4 Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives ABABABABAABB. Test the sequence for randomness about the median with a 5% level of significance. Verify that the number of runs is 10. What is the upper critical value c2? arrow_forwardSand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 34.4 27.1 30.8 28.0 32.2 27.6 32.8 25.2 31.4 33.5 24.7 28.4 Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives ABABABABAABB. Test the sequence for randomness about the median with a 5% level of significance. Verify that the number of runs is 10. What is the upper critical value c2?arrow_forward29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.arrow_forward
- Sand and clay studies were conducted at a site in California. Twelve consecutive depths, each about 15 cm deep, were studied and the following percentages of sand in the soil were recorded. 27.3 34.6 30.6 27.8 33.4 31.5 27.3 31.2 32.0 24.7 24.4 28.2 Test this sequence for randomness about the median. Converting this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B denotes a value below the median gives BAABAABAABBB. Verify that the number of runs is 7, the lower critical number is 3, and the upper critical number is 11. Use a 5% level of significance. State the conclusion of the test and interpret your results.arrow_forward29% of all college students major in STEM (Science, Technology, Engineering, and Math). If 46 college students are randomly selected, find the probability thata. Exactly 11 of them major in STEM. b. At most 12 of them major in STEM. c. At least 11 of them major in STEM. d. Between 11 and 15 (including 11 and 15) of them major in STEM.arrow_forward4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.arrow_forward
- 3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.arrow_forward2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…arrow_forwardPlease solving problem2 Problem1 We consider a two-period binomial model with the following properties: each period lastsone (1) year and the current stock price is S0 = 4. On each period, the stock price doubleswhen it moves up and is reduced by half when it moves down. The annual interest rateon the money market is 25%. (This model is the same as in Prob. 1 of HW#2).We consider four options on this market: A European call option with maturity T = 2 years and strike price K = 5; A European put option with maturity T = 2 years and strike price K = 5; An American call option with maturity T = 2 years and strike price K = 5; An American put option with maturity T = 2 years and strike price K = 5.(a) Find the price at time 0 of both European options.(b) Find the price at time 0 of both American options. Compare your results with (a)and comment.(c) For each of the American options, describe the optimal exercising strategy.arrow_forward
- Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forwardThis question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one. A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture. A B A B at some instant, the piston will be tangent to the circle (a) Express the x and y coordinates of point A as functions of t: x= 2 cos(3πt) and y= 2 sin(3t) (b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds: -cot(3πt) sin(3лt) (c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +411- 4 -2 sin (3лt) (d)…arrow_forward5. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.AE.003. y y= ex² 0 Video Example x EXAMPLE 3 (a) Use the Midpoint Rule with n = 10 to approximate the integral कर L'ex² dx. (b) Give an upper bound for the error involved in this approximation. SOLUTION 8+2 1 L'ex² d (a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.) dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)] 0.1 [0.0025 +0.0225 + + e0.0625 + 0.1225 e0.3025 + e0.4225 + e0.2025 + + e0.5625 €0.7225 +0.9025] The figure illustrates this approximation. (b) Since f(x) = ex², we have f'(x) = 0 ≤ f'(x) = < 6e. ASK YOUR TEACHER and f'(x) = Also, since 0 ≤ x ≤ 1 we have x² ≤ and so Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final answer to five decimal places.) 6e(1)3 e 24( = ≈arrow_forward
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