Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 7 - Section 7.6 - Linear Programming - Exercise Set - Page 874: 33

Answer

stocks $5000$ dollars, bonds $5000$ dollars.
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Work Step by Step

Step 1. Assume that the amount invested in stocks is $x$ dollars, and in bonds is $y$ dollars. Step 2. Based on the given conditions, we have $\begin{cases} x+y\leq10,000\\y\geq3000\\x\geq2000\\y\geq x \end{cases}$ Step 3. The equation for the returns can be expressed as $R=0.12x + 0.08y$ Step 4. To maximize the return, graph the inequalities as shown and we can identify the corners of the solution region as: $(2000,3000), (3000,3000),(2000,8000), (5000,5000)$. Step 5. Check the value of the corner points with the return equation. We have $R_1=0.12(2000) + 0.08(3000)=480$; $R_2=0.12(3000) + 0.08(3000)=600$; $R_3=0.12(2000) + 0.08(8000)=880$; $R_4=0.12(5000) + 0.08(5000)=1000$; Step 6. We conclude that the amount invested in stocks should be $5000$ dollars, and in bonds should be $5000$ dollars to maximize the return.
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