Explanation Given Information: The provided table is, Price ($) Dividend Yield (%) 52 - week price change ($) DUK (Duke Energy Corp) 80 4 4 DTV (DIRECTV) 100 0 10 OCR (Omnicare, NC.) 90 1 30 Let x represent number of shares of DUK, y represents the number of shares of DTV and z represents the number of shares of OCR. Thus, the maximum gain is given by p = 4 x + 30 y + 30 z , measured in hundreds of dollars. And, the constraints are, 80 x + 100 y + 90 z ≤ 90 , 000 32 x + 9 z ≤ 9000 x ≥ 0 , y ≥ 0 , z ≥ 0 Consider the maximisation problem. Maximize p = 4 x + 10 y + 30 z Subject to 80 x + 100 y + 90 z ≤ 90 , 000 32 x + 9 z ≤ 9000 x ≥ 0 , y ≥ 0 , z ≥ 0 Step 1: Use slack variables and write the inequalities in equation form. Add the slack variables s and t . 80 x + 100 y + 90 z + s = 90 , 000 32 x + 9 z + t = 9000 Step 2: Write the equations in an augmented matrix. The equations are, 80 x + 100 y + 90 z + s = 90 , 000 32 x + 9 z + t = 9000 And, − 20 x − 15 y − 5 z + p = 0 Write the equations in augmented matrix as below, x y z s t p s 80 100 90 1 0 0 90000 t 32 0 9 0 1 0 9000 p − 4 − 30 − 30 0 0 1 0 Step 3: Choose the smallest negative number on the left side of the bottom row and pivot the column. Since, the smallest negative number on the left side of the bottom row is − 30 . Thus, choose the left most entry and pivot the y column. Step 4: Select the pivot which is the smallest of the test ratios a b , where a is the entry in the right most column and b is the corresponding entry in the pivot column. Since, the test ratios are neither 0 nor negative. Thus, the test ratios are 90 , 000 100 = 900 . Thus, the pivot is 100 in column y as below, x y z s t p s 80 100 90 1 0 0 90000 t 32 0 9 0 1 0 9000 p − 4 − 30 − 30 0 0 1 0 Step 5: Clear the pivot column using the pivot and label the pivot row with the label of the pivot column

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.3, Problem 38E

To determine

Whether the investment in DTV stock maximize the 52-week gain and for tax reasons earning no more than $900 in dividends where the total investment is up to $90,000 in DUK, DTV and OCR shares and the table represents data of various shares and assume that the 52 week change in DTV stock is $30 but its price is unchanged.

Price ($) Dividend Yield (%) 52- week price change ($)

DUK (Duke Energy Corp) 80 4 4

DTV (DIRECTV) 100 0 10

OCR (Omnicare, NC.) 90 1 30

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Chapter 5.3, Problem 37E

Chapter 5.3, Problem 39E

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	Price ($)	Dividend Yield (%)	52- week price change ($)
DUK (Duke Energy Corp)	80	4	4
DTV (DIRECTV)	100	0	10
OCR (Omnicare, NC.)	90	1	30

Solution Summary: The author explains that the maximum gain in DTV stock is 30,000 but its price is unchanged.

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