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

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

7th Edition

ISBN: 9781337291484

Author: Waner

Publisher: Cengage

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 6, Problem 36RE

To determine

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 35RE

Chapter 6, Problem 37RE

Students have asked these similar questions

The spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.

Find the indefinite integral. Check Answer: 7x 4 + 1x dx

show sketch

Chapter 6 Solutions

Finite Mathematics and Application Calculus (Looseleaf) - Text Only

Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

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.

Want to see the full answer?

Chapter 6 Solutions