College Algebra
7th Edition
ISBN: 9781305115545
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: Cengage Learning
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Chapter 5.2, Problem 39E
Financial Planning Mark has $100,000 to invest. His Financial consultant advises him to diversify his investment in three types of bonds: short-term, Intermediate-term, and long-term. The short-term bonds pay 4%, the intermediate term bonds pay 5%, and the long-term bonds pay 6% simple interest per year. Mark wishes to realize a total annual income of 5.1 % with equal amounts invested in short - and intermediate-term bonds. How much should he invest in each type of bond?
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George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 8% for the bond fund and 20% for the stock fund. Whatever portion of the inheritance George finally decides to commit to the trust fund, he wants to invest at least 40% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 5.5%.
Formulate a linear programming model that can be used to determine the percentage that should be allocated to each of the possible investment alternatives. If required, round your answers to three decimal places.
Let B
=
percentage of funds invested in the bond fund
S
=
percentage of funds invested in the stock fund
Max
0.08 B
+
0.20 S
s.t.
1B
≥
..................
Bond…
George Johnson recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock
fund. The projected returns over the life of the investments are 11% for the bond fund and 15% for the stock fund. Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest
at least 30% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 12.5%.
(a) Formulate a linear programming model that can be used to determine the percentage (as a decimal) that should be allocated to each of the possible investment alternatives. (Assume B is the percentage (as a
decimal) of funds invested in the bond fund and S is the percentage (as a decimal) of funds invested in the stock fund.)
Max (as a decimal)
s.t.
bond minimum fund
minimum return
percentage requirement
B, S≥ 0…
You are considering in investing one of the two options: Investment A requires a $80,000 upfront payment and generates $59,000 annually, Investment B requires a $68,000 upfront payment. How much should Investment B generate annually so that the total returns from Investment A and B become equal after 3 years?
Chapter 5 Solutions
College Algebra
Ch. 5.1 - The system of equations {2x+3y=75xy=9} is a system...Ch. 5.1 - A system of equation in two variable can be solved...Ch. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...
Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Graphical Method Two equations and their graphs...Ch. 5.1 - Graphical Method Two equations and their graphs...Ch. 5.1 - Number of solutions determined Graphically Graph...Ch. 5.1 - Number of solutions determined Graphically Graph...Ch. 5.1 - Number of solutions determined Graphically Graph...Ch. 5.1 - Number of solutions determined Graphically Graph...Ch. 5.1 - Number of solutions determined Graphically Graph...Ch. 5.1 - Prob. 20ECh. 5.1 - Solving a system of equations Solve the system, or...Ch. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Solving a system of equations Solve the system, or...Ch. 5.1 - Solving a system of equations Solve the system, or...Ch. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Solving a system of equations Solve the system, or...Ch. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Solving a system of equations Solve the system, or...Ch. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Value of coin A man has 14 coins in his pocket,...Ch. 5.1 - Admission Fees The admission fee at an amusement...Ch. 5.1 - Gas Station A gas Station sells regular gas for...Ch. 5.1 - Prob. 64ECh. 5.1 - Airplane Speed A man flies a small airplane from...Ch. 5.1 - Prob. 66ECh. 5.1 - Nutrition A researcher performs an experiment to...Ch. 5.1 - Prob. 68ECh. 5.1 - Prob. 69ECh. 5.1 - Mixture problem A biologist has two brine...Ch. 5.1 - Prob. 71ECh. 5.1 - Investments A man invests his savings in two...Ch. 5.1 - Prob. 73ECh. 5.1 - Aerobic exercise a woman is spitfire by cycling...Ch. 5.1 - Prob. 75ECh. 5.1 - Prob. 76ECh. 5.1 - Prob. 77ECh. 5.2 - These exercises refer to the following system: If...Ch. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Triangular system Use back Substitution to solve...Ch. 5.2 - Triangular system Use back substitution to solve...Ch. 5.2 - Triangular system Use back substitution to solve...Ch. 5.2 - Triangular Systems Use back-substitution to solve...Ch. 5.2 - Triangular system Use back substitution to solve...Ch. 5.2 - Triangular Systems Use Back substitution to solve...Ch. 5.2 - Eliminating a variable Perform an operation on the...Ch. 5.2 - Eliminating a variable perform and operation on...Ch. 5.2 - Eliminating a variable perform an operation on the...Ch. 5.2 - Eliminating a variable Perform an operation on the...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Solving a system of equation in three variables...Ch. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - Financial Planning Mark has $100,000 to invest....Ch. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Diet Program Nicole started a new diet that...Ch. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.3 - Prob. 1ECh. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Prob. 8ECh. 5.3 - Prob. 9ECh. 5.3 - Prob. 10ECh. 5.3 - Prob. 11ECh. 5.3 - Prob. 12ECh. 5.3 - Prob. 13ECh. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Prob. 16ECh. 5.3 - Prob. 17ECh. 5.3 - Prob. 18ECh. 5.3 - Prob. 19ECh. 5.3 - Prob. 20ECh. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.4 - The system of equations {2yx2=0yx=4} Is graph...Ch. 5.4 - The system of equations {2yx2=0yx=4} Is graphed...Ch. 5.4 - Substitutions method Use the substitution method...Ch. 5.4 - Substitution method Use the substitution method to...Ch. 5.4 - Substitution Method Use the substitution method to...Ch. 5.4 - Substitution Method Use the substitution method to...Ch. 5.4 - Substitution Method Use the substitution method to...Ch. 5.4 - Substitution Method Use the substitution method to...Ch. 5.4 - Elimination Method Use the elimination method to...Ch. 5.4 - Elimination Method Use the elimination method to...Ch. 5.4 - Elimination method Use the elimination method to...Ch. 5.4 - Elimination Method Use the elimination method to...Ch. 5.4 - Elimination method Use the elimination method to...Ch. 5.4 - Elimination Method Use the elimination method to...Ch. 5.4 - Finding intersection points graphically two...Ch. 5.4 - Finding intersection points graphically two...Ch. 5.4 - Finding intersection points graphically two...Ch. 5.4 - Finding intersection points graphically two...Ch. 5.4 - Solving Nonliear Systems Find all solutions of the...Ch. 5.4 - Solving Nonliear Systems Find all solutions of the...Ch. 5.4 - Solving Nonliear Systems Find all solutions of the...Ch. 5.4 - Solving Nonliear Systems Find all solutions of the...Ch. 5.4 - Solving Nonliear Systems Find all solutions of the...Ch. 5.4 - Solving Nonliear Systems Find all solutions of the...Ch. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Solving Nonlinear system Find all solutions of the...Ch. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.5 - Prob. 1ECh. 5.5 - To graph an inequality, we first graph the...Ch. 5.5 - Prob. 3ECh. 5.5 - Prob. 4ECh. 5.5 - Prob. 5ECh. 5.5 - Prob. 6ECh. 5.5 - Prob. 7ECh. 5.5 - Prob. 8ECh. 5.5 - Prob. 9ECh. 5.5 - Prob. 10ECh. 5.5 - Prob. 11ECh. 5.5 - Graphing Inequalities Graph the inequality x1Ch. 5.5 - Graphing Inequalities Graph the inequality x2Ch. 5.5 - Prob. 14ECh. 5.5 - Prob. 15ECh. 5.5 - Prob. 16ECh. 5.5 - Prob. 17ECh. 5.5 - Prob. 18ECh. 5.5 - Prob. 19ECh. 5.5 - Prob. 20ECh. 5.5 - Prob. 21ECh. 5.5 - Prob. 22ECh. 5.5 - Prob. 23ECh. 5.5 - Graphing inequalities Use a Graphing calculator to...Ch. 5.5 - Graphing inequalities Use a Graphing calculator to...Ch. 5.5 - Prob. 26ECh. 5.5 - Prob. 27ECh. 5.5 - Prob. 28ECh. 5.5 - Prob. 29ECh. 5.5 - Prob. 30ECh. 5.5 - Systems of Inequalities Graph the solutions set of...Ch. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Prob. 35ECh. 5.5 - Systems of Inequalities Graph the solutions set of...Ch. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Prob. 39ECh. 5.5 - Prob. 40ECh. 5.5 - Prob. 41ECh. 5.5 - Prob. 42ECh. 5.5 - Prob. 43ECh. 5.5 - Prob. 44ECh. 5.5 - Prob. 45ECh. 5.5 - Prob. 46ECh. 5.5 - Prob. 47ECh. 5.5 - Prob. 48ECh. 5.5 - Prob. 49ECh. 5.5 - Prob. 50ECh. 5.5 - Prob. 51ECh. 5.5 - Prob. 52ECh. 5.5 - Prob. 53ECh. 5.5 - Prob. 54ECh. 5.5 - Prob. 55ECh. 5.5 - Prob. 56ECh. 5.5 - Prob. 57ECh. 5.5 - Prob. 58ECh. 5.5 - Prob. 59ECh. 5.5 - Prob. 60ECh. 5.5 - Prob. 61ECh. 5.5 - Prob. 62ECh. 5.5 - Prob. 63ECh. 5.5 - Prob. 64ECh. 5.5 - Prob. 65ECh. 5.5 - Prob. 66ECh. 5.5 - Prob. 67ECh. 5.5 - Graphing Systems in inequalities Use a graphing...Ch. 5.5 - Prob. 69ECh. 5.5 - Prob. 70ECh. 5.5 - Prob. 71ECh. 5.5 - Prob. 72ECh. 5.5 - Coffee Blends A coffee merchant sells two...Ch. 5.5 - Prob. 74ECh. 5.5 - Discuss Shading unwanted regions to graph the...Ch. 5 - Prob. 1CCCh. 5 - Prob. 2CCCh. 5 - Prob. 3CCCh. 5 - Prob. 4CCCh. 5 - Prob. 5CCCh. 5 - (a) Explain how Gaussian elimination works. (b)...Ch. 5 - (a) How do we express a rational function r as a...Ch. 5 - Prob. 8CCCh. 5 - (a) How do we graph the solution set of a system...Ch. 5 - Prob. 1ECh. 5 - Systems Of linear Equations in two Variables Solve...Ch. 5 - Prob. 3ECh. 5 - Prob. 4ECh. 5 - Prob. 5ECh. 5 - Prob. 6ECh. 5 - Prob. 7ECh. 5 - Prob. 8ECh. 5 - Prob. 9ECh. 5 - Prob. 10ECh. 5 - Prob. 11ECh. 5 - Prob. 12ECh. 5 - Prob. 13ECh. 5 - Prob. 14ECh. 5 - Prob. 15ECh. 5 - Prob. 16ECh. 5 - Prob. 17ECh. 5 - Prob. 18ECh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Prob. 43ECh. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Graphing Inequalities Graph the inequality xy24Ch. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - General System of equations for what Values of k...Ch. 5 - A system of equations if given. (a) Determine...Ch. 5 - A system of equation is given. (a) Determine...Ch. 5 - Prob. 3TCh. 5 - Prob. 4TCh. 5 - Prob. 5TCh. 5 - Prob. 6TCh. 5 - Prob. 7TCh. 5 - Prob. 8TCh. 5 - Prob. 9TCh. 5 - Prob. 10TCh. 5 - Prob. 11TCh. 5 - Prob. 12TCh. 5 - Prob. 13TCh. 5 - Prob. 14TCh. 5 - Prob. 15TCh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Find the maximum and minimum values of the given...Ch. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Manufacturing Calculators A manufacturer of...Ch. 5 - Prob. 9PCh. 5 - Prob. 10PCh. 5 - Prob. 11PCh. 5 - Feeding Lab Rabbits A biologist wishes to feed...Ch. 5 - Investing in Bonds A woman wishes to invest...Ch. 5 - Annual interest yield refer to problem 13 .suppose...Ch. 5 - Business Strategy A small software company...Ch. 5 - Feasible region all part of this problem refer to...
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