Explanation Given Information: CNM shares cost $40, and yield 5.5% in dividends having risk index of 1.0. SS shares cost $25, and yield 7.5% in dividends having risk index of 1.5. Also minimum earning should be $1650 and maximum investment can be $30000. Formula used: 1: Plot the constraint equations on the graph. 2: Test the feasibility of the inequality. 3: Shade the outside of the rectangle so as to define a new bounded feasible region and locate the new corner points. 4: Obtain the value of objective function at the corner points. 5: If the optimal solution occur at the one of the corner points, then LP problem has that corner point as optimal solution otherwise it has no optimal solution. Calculation: Consider the provided information that CNM shares cost $40, and yield 5.5% in dividends having risk index of 1.0. SS shares cost $25, and yield 7.5% in dividends having risk index of 1.5. Let the number of shares bought from CNM and SS be x , y respectively. Thus, the total risk index function will be c = x + 1.5 y . Also, minimum earning should be $1650 and maximum investment can be $30000. Thus the constraints will be 40 x + 25 y ≤ 300 0 0 2.2 x + 1.875 y ≥ 1 6 5 0 x ≥ 0 y ≥ 0 Consider the first constraint equation, 40 x + 25 y = 300 0 0 Isolate the variable y , by subtracting 40 x from both sides, 40 x − 40 x + 25 y = 300 0 0 − 4 0 x y = 1 25 ( 30000 − 40 x ) To plot the graph of the function, find the ordered pairs of the first constraint equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 1 25 ( 30000 − 40 ( 0 ) ) = 30000 25 = 1200 For x = 100 , substitute 100 for x , y = 1 25 ( 30000 − 40 ( 100 ) ) = 26000 25 = 1040 Construct a table for the ordered pairs, x 0 100 y 1200 1040 Test the first inequality by (0,0) test coordinates. 40 ( 0 ) + 25 ( 0 ) ≤ 300 0 0 0 ≤ 300 0 0 The inequality is satisfied. If the test point satisfies the inequality then the set of solutions is the line plus the entire region on the side of the line i.e. towards the test coordinate (0, 0). Consider the second constraint equation. 2.2 x + 1.875 y = 1650 Isolate the variable y , by subtracting 2.2 x from both sides, 1.875 y = 1650 − 2.2 x y = 1 1.875 ( 1650 − 2.2 x ) To plot the graph of the function, find the ordered pairs of the second constraint equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 1 1.875 ( 1650 − 2.2 ( 0 ) ) = 1650 1.875 = 880 For x = 100 , substitute 100 for x , y = 1 1.875 ( 1650 − 2.2 ( 100 ) ) = 1430 1.875 = 762.66 Construct a table for the ordered pairs of second constraint equation, x 0 100 y 880 762.66 Test the second inequality by (0, 0) test coordinates. 2.2 x + 1.875 y ≥ 1 6 5 0 2.2 ( 0 ) + 1

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5, Problem 36RE

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To calculate: The minimum total risk index and the number of shares of each stock to be bought to earn atleast $1650 by investing maximum $30000. CNM shares cost $40, and yield 5.5% in dividends having risk index of 1.0. SS shares cost $25, and yield 7.5% in dividends having risk index of 1.5.

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Chapter 5, Problem 35RE

Chapter 5, Problem 37RE

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The minimum total risk index and the number of shares of each stock to be bought to earn atleast $1650 by investing maximum $30000. CNM shares cost $40, and yield 5.5% in dividends having risk index of 1.0. SS shares cost $25, and yield 7.5% in dividends having risk index of 1.5.

Solution Summary: The author calculates the minimum risk index and number of shares of each stock to be bought to earn atleast 1650 by investing maximum 30000.

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To calculate: The minimum total risk index and the number of shares of each stock to be bought to earn atleast $1650 by investing maximum $30000. CNM shares cost $40, and yield 5.5% in dividends having risk index of 1.0. SS shares cost $25, and yield 7.5% in dividends having risk index of 1.5.

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