Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
14th Edition
ISBN: 9780134677972
Author: Barnett
Publisher: PEARSON
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Textbook Question
Chapter 5.3, Problem 33E
Solve the linear programming problems stated in Problems 17-38.
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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.
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.
This 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)…
Chapter 5 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Ch. 5.1 - In Step 2 of Example 1, 0,0 was used as a test...Ch. 5.1 - Graph 6x3y18.Ch. 5.1 - Graph (A) y4 (B) 4x9 (C) 3x2yCh. 5.1 - Find the linear inequality whose graph is given in...Ch. 5.1 - A food vendor at a rock concert sells hot dogs for...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...
Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - For Problems 1-8, if necessary, review Section...Ch. 5.1 - Graph each inequality in Problems 9-18. yx1Ch. 5.1 - Graph each inequality in Problems 9-18. yx+1Ch. 5.1 - Graph each inequality in Problems 9-18. 3x2y6Ch. 5.1 - Graph each inequality in Problems 9-18. 2x5y10Ch. 5.1 - Graph each inequality in Problems 9-18. x4Ch. 5.1 - Graph each inequality in Problems 9-18. y5Ch. 5.1 - Graph each inequality in Problems 9-18. 6x+4y24Ch. 5.1 - Graph each inequality in Problems 9-18. 4x+8y32Ch. 5.1 - Graph each inequality in Problems 9-18. 5x2yCh. 5.1 - Graph each inequality in Problems 9-18. 6x4yCh. 5.1 - In Problems 19-22, (A) graph the set of points...Ch. 5.1 - In Problems 19-22, (A) graph the set of points...Ch. 5.1 - In Problems 19-22, (A) graph the set of points...Ch. 5.1 - In Problems 19-22, (A) graph the set of points...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - \ In Problems 23-32, define the variable and...Ch. 5.1 - In Problems 23-32, define the variable and...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Exercises 33-38, state the linear inequality...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 39-44, define two variables and...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 45-54, graph each inequality subject...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.1 - In Problems 55-66, express your answer as a linear...Ch. 5.2 - Determine whether the solution region of each...Ch. 5.2 - Solve the following system of linear inequalities...Ch. 5.2 - Solve the following system of linear inequalities...Ch. 5.2 - A manufacturing plant makes two types of...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - For Problems 1-8, if necessary, review Section...Ch. 5.2 - In Problems 9-12, match the solution region of...Ch. 5.2 - In Problems 9-12, match the solution region of...Ch. 5.2 - In Problems 9-12, match the solution region of...Ch. 5.2 - In Problems 9-12, match the solution region of...Ch. 5.2 - In Problems 13-16, solve each system of linear...Ch. 5.2 - In Problems 13-16, solve each system of linear...Ch. 5.2 - In Problems 13-16, solve each system of linear...Ch. 5.2 - In Problems 13-16, solve each system of linear...Ch. 5.2 - In Problems 17-20, match the solution region of...Ch. 5.2 - In Problems 17-20, match the solution region of...Ch. 5.2 - In Problems 17-20, match the solution region of...Ch. 5.2 - In Problems 17-20, match the solution region of...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - In Problems 21-28, is the solution region bounded...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 29-38 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - \ Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Solve the systems in Problems 39-48 graphically...Ch. 5.2 - Problems 49 and 50 introduce an algebraic process...Ch. 5.2 - Problems 49 and 50 introduce an algebraic process...Ch. 5.2 - Water skis. A manufacturing company makes two...Ch. 5.2 - Furniture. A furniture manufacturing company...Ch. 5.2 - Water skis. Refer to Problem 51. The company makes...Ch. 5.2 - Furniture. Refer to Problem 52. The company makes...Ch. 5.2 - Plant food. A farmer can buy two types of plant...Ch. 5.2 - Nutrition. A dietician in a hospital is to arrange...Ch. 5.2 - Psychology. A psychologist uses two types of boxes...Ch. 5.3 - A manufacturing plant makes two types of...Ch. 5.3 - Refer to the feasible region S shown in Figure 3....Ch. 5.3 - In Example 2B we saw that there was no optimal...Ch. 5.3 - (A) Maximize and minimize z=4x+2y subject to the...Ch. 5.3 - A chicken farmer can buy a special food mix A at...Ch. 5.3 - In Problem 1-8, if necessary, review Theorem 1. In...Ch. 5.3 - In Problem 1-8, if necessary, review Theorem 1. In...Ch. 5.3 - In Problem 1-8, if necessary, review Theorem 1. In...Ch. 5.3 - In Problem 1-8, if necessary, review Theorem 1. In...Ch. 5.3 - In Problems 1-8, if necessary, review Theorem 1....Ch. 5.3 - In Problems 1-8, if necessary, review Theorem 1....Ch. 5.3 - In Problems 1-8, if necessary, review Theorem 1....Ch. 5.3 - In Problems 1-8, if necessary, review Theorem 1....Ch. 5.3 - In Problems 9-12, graph the constant-profit lines...Ch. 5.3 - In Problems 9-12, graph the constant-profit lines...Ch. 5.3 - In Problems 9-12, graph the constant-profit lines...Ch. 5.3 - In Problems 9-12, graph the constant-profit lines...Ch. 5.3 - In Problems 13-16, graph the constant-cost lines...Ch. 5.3 - In Problems 13-16, graph the constant-cost lines...Ch. 5.3 - In Problems 13-16, graph the constant-cost lines...Ch. 5.3 - In Problems 13-16, graph the constant-cost lines...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - Solve the linear programming problems stated in...Ch. 5.3 - In Problems 39 and 40, explain why Theorem 2...Ch. 5.3 - In Problems 39 and 40, explain why Theorem 2...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - Problems 41-48 refer to the bounded feasible...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5.3 - In Problems 49-64, construct a mathematical model...Ch. 5 - Graph each inequality. x2y3Ch. 5 - Graph each inequality. 3y5x30Ch. 5 - Graph the systems in Problems 3-6 and indicate...Ch. 5 - Graph the systems in Problems 3-6 and indicate...Ch. 5 - Graph the systems in Problems 3-6 and indicate...Ch. 5 - Graph the systems in Problems 3-6 and indicate...Ch. 5 - In Exercises 7 and 8, state the linear inequality...Ch. 5 - In Exercises 7 and 8, state the linear inequality...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Solve the linear programming problems in Problems...Ch. 5 - Electronics. 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- 5. [-/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_forward1. Consider the following preference ballots: Number of voters Rankings 6 5 4 2 1st choice A DCB DC 2nd choice B B D 3rd choice DCBD 4th choice CA AAA For each of the four voting systems we have studied, determine who would win the election in each case. (Remember: For plurality with runoff, all but the top two vote-getters are simultaneously eliminated at the end of round 1.)arrow_forwardPractice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forward
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