Explanation Given Information: Price($) Dividend (%) 52- week Price change($) OCR(Omnicare) 90 1 28 RCKY(Rocky Brands) 20 2 6 GCO(Genesco) 70 0 -5 ATVI(Activision Blizzard) 25 1 5 Formula used: The steps for Linear Programming problems: 1. To make the corner points are inside the rectangle draw a rectangle large enough. 2. Shade the outside of the rectangle so that a new bounded feasible region can be defined and locate the new corner points. 3. Obtain the optimal solutions by the use of bounded feasible region. 4. If the optimal solution occurs at the one of the corner points, then only LP problem has that corner point as the optimal solution otherwise it has no optimal solution. Calculation: Consider the number of OCR shares to be x. Consider the number of RCKY shares to be y. 90 x + 20 y ≤ 10000 0.01 ⋅ 90 x + 0.02 ⋅ 20 y ≥ 120 The constraints include that x ≥ 0 , y ≥ 0 because number of OCR shares and RCKY shares cannot be negative. Minimize p = 28 x + 6 y subject to the given following constraints 90 x + 20 y ≤ 10000 , 0.01 ⋅ 90 x + 0.02 ⋅ 20 y ≥ 120 and x ≥ 0 , y ≥ 0 . Consider the first constraint equation, 90 x + 20 y = 10000 Isolate the variable y , by subtracting 90 x from both sides, 90 x − 90 x + 20 y = 10000 − 90 x 20 y = 10000 − 90 x y = ( 10000 − 90 x ) 20 y = 500 − 4.5 ⋅ x To plot the graph of the function, find the ordered pairs of the equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 500 − 4.5 ⋅ x = 500 − 4.5 ⋅ 0 = 500 − 0 = 500 For x = 1 , substitute 1 for x , y = 500 − 4 x = 500 − 4.5 ⋅ 100 = 500 − 450 = 5 For x = 2 , substitute 2 for x , y = 500 − 4 x = 500 − 4.5 ⋅ 200 = 500 − 900 = − 400 Construct a table for the ordered pairs, x 0 100 200 y 500 5 -400 Test the first inequality by ( 0 , 0 ) test coordinates. 90 x + 20 y ≤ 10000 90 ⋅ 0 + 20 ⋅ 0 ≤ ? 10000 0 + 0 ≤ ? 10000 0 < 10000 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 same side of the line as the test coordinate ( 0 , 0 ) . Consider the second constraint equation. 0.01 ⋅ 90 x + 0.02 ⋅ 20 y = 120 0.9 x + 0.4 y = 120 Isolate the variable y , by subtracting 0.9 x from both sides, 0.9 x − 0.9 x + 0.4 y = 120 − 0.9 x 0.4 y = 120 − 0.9 x y = ( 120 − 0.9 x ) 0.4 y = 10 ⋅ ( 120 − 0.9 x ) 4 On further solving the equation, y = ( 1200 − 9 x ) 4 y = 300 − 9 4 ⋅ 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 = 300 − 9 4 ⋅ 0 = 300 − 0 = 300 For x = 40 , substitute 40 for x , y = 300 − 9 4 ⋅ 40 = 300 − 9 ⋅ 10 = 300 − 90 = 210 For x = 80 , substitute 80 for x , y = 300 − 9 4 ⋅ 80 = 300 − 9 ⋅ 20 = 300 − 180 = 120 Construct a table for the ordered pairs of second constraint equation, x 0 40 80 y 300 210 120 Test the second inequality by ( 0 , 0 ) test coordinates

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ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.2, Problem 41E

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To calculate: The number of shares of OCR and RCKY the person should purchase to minimize the 52-week gain.

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Chapter 5.2, Problem 40E

Chapter 5.2, Problem 42E

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The number of shares of OCR and RCKY the person should purchase to minimize the 52-week gain.

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