Explanation Given information: Portia has to invest $10,000. She is considering a certificate of deposit (CD) that is expected to yield 5%, a mutual fund expected to yield 7%, and stocks expected to yield 9%. The amount invested in the mutual fund can be no more than the amount invested in the CD and stocks together. The amount availability to invest in the mutual fund and stocks must not be more than $8000. Formula used: To draw the graph of inequality y ≥ m x + b or y ≤ m x + b , then use the steps: Step 1: Draw the graph of y = m x + b . Step 2: The graph of y ≥ m x + b consists of all points above or on the line, and y ≤ m x + b consists of all points below or on the line. Calculation: Let she invests her fund in CD, mutual fund and stock which is x , y and z . But, the amount availability to invest is $10000. So, x + y + z = 10000 z = 10000 − x − y The amount invested in the mutual fund can be no more than the amount invested in the CD and stocks together. So, y ≤ x + z y ≤ x + 10000 − x − y 2 y ≤ 10000 y ≤ 5000 As, the amount in the mutual fund and stocks must be no more than $8000. y + z ≤ 8000 y + 10000 − x − y ≤ 8000 x ≥ 2000 Also, x ≤ 10 , 000 , y ≤ 10 , 000 and x ≥ 0 , y ≥ 0 . Therefore, constraints equations are: { y ≤ 5000 x ≥ 2000 x ≤ 10 , 000 x ≥ 0 , y ≥ 0 The returns of funds from CD is 5%, 7% from mutual fund and 9% from stocks so, M = 0.05 x + 0.07 y + 0.09 z M = 0.05 x + 0.07 y + 0.09 ( 10 , 000 − x − y ) M = 900 − 0.04 x − 0.02 y So, the objective function is: Maximize: M = 900 − 0

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 3, Problem 11RE

To determine

To calculate: The amount of Portia should invest in each investment vehicle to maximize her total expected yield and Portia has to invest $10,000.So, she is considering a certificate of deposit (CD) that is expected to yield 5%, a mutual fund expected to yield 7%, and stocks expected to yield 9% on the amount invested in the mutual fund can be no more than the amount invested in the CD and stocks together. The amount availability to invest in the mutual fund and stocks must not be more than $8000.

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Chapter 3, Problem 10RE

Chapter 3, Problem 12RE

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Finite Mathematics & Its Applications (12th Edition)

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Solution Summary: The author explains how Portia should invest in each investment vehicle to maximize her total expected yield.

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