Explanation Given: An investor makes 3 types of investments. The details can be reproduced in the following table: Types and Return of investments Oil leases Stocks Safe bond Variables x 1 x 2 x 3 50,000 % of investment combined 1 1 ≤ 30 % of investment combined 1 1 ≤ 50 Return on investment (%) 15 9 5 z Explanation The table summarizes the information of the company. Types and return of investments Oil leases Stocks Safe bond Variables x 1 x 2 x 3 50,000 % of investment combined 1 1 ≤ 30 % of investment combined 1 1 ≤ 50 Return on investment (%) 15 9 5 z The maximization problem can be stated as follows: Maximize z = 15 x 1 + 9 x 2 + 5 x 3 Subject to x 1 + x 2 + x 3 ≤ 50 , 000 x 1 + x 2 ≤ 15 , 000 x 1 + x 3 ≤ 25 , 000 with x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 The problem has 3 constraints, with “at most” ( ≤ ) values, for the objective function. We need 3 slack variables to make them linear equation. Adding slack variable s 1 to 15 x 1 + 10 x 2 + 8 x 3 ≤ 1500 : 15 x 1 + 10 x 2 + 8 x 3 + s 1 = 1500 Adding slack variable s 2 to 5 x 1 + 4 x 2 + 4 x 3 ≤ 2700 , 5 x 1 + 4 x 2 + 4 x 3 + s 2 = 2700 Adding slack variable s 3 to 5 x 1 + 4 x 2 + 4 x 3 ≤ 2700 : 6 x 1 + 5 x 2 + 5 x 3 + s 3 = 1200 Rewriting the objective function: − 15 x 1 − 9 x 2 − 5 x 3 + z = 0 Initial simplex tableau is as follows: [ x 1 x 2 x 3 s 1 s 2 s 3 z 1 1 1 1 0 0 0 50 , 000 1 1 0 0 1 0 0 15 , 000 1 0 1 0 0 1 0 25 , 000 − 15 − 9 − 5 0 0 0 1 0 ] The solutions from the simplex tableau are not optimum. To get maximum of the function, pivot procedure is applied till all the indictors are nonnegative and solutions are read from the tableau. Step 1: Find the largest negative indicator (number in the last row) because it indicates the variable with the largest coefficient in the objective function. It becomes the pivot column. From the above tableau, − 15 is the largest negative number. Step 2: The smallest quotient formed by dividing each number in the pivot column from the right side of the tableau of the corresponding row becomes the pivot row. Corresponding quotients: 50 , 000 1 = 50 , 000 15 , 000 1 = 15 , 000 25 , 000 1 = 25 , 000 Quotient 15,000 is the smallest, specifying 1 as the pivot in the 2nd row, 1st column: [ x 1 x 2 x 3 s 1 s 2 s 3 z 1 1 1 1 0 0 0 50 , 000 1 1 0 0 1 0 0 15 , 000 1 0 1 0 0 1 0 25 , 000 − 15 − 9 − 5 0 0 0 1 0 ] Perform row operations to make all zeros except pivot in the x 1 column

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4, Problem 42RE

To determine

Solve the maximization problem for the investment problem in Exercise 38.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 41RE

Chapter 4, Problem 43RE

Students have asked these similar questions

2) Suppose you start with $60 and increase this amount by 15%. Since 15% of $60 is $9, that means you increase your $60 by $9, so you now have $69. Notice that we did this calculation in two steps: first we multiplied $60 by 0.15 to find 15% of $60, then we added this amount to our original $60. Explain why it makes sense that increasing $60 by 15% can also be accomplished in one step by multiplying $60 times 1.15. 3) Suppose you have $60 and want to decrease this amount by 15%. Since 15% of $60 is $9, that means you will decrease your $60 by $9, so you now have $51. Notice that we did this calculation in two steps: first we multiplied $60 by 0.15 to find 15% of $60, then we subtracted this amount from our original $60. Explain why it makes sense that decreasing $60 by 15% can also be accomplished in one step by multiplying $60 times 0.85. 4) In the Read and Study section, we noted that the population in Colony B is increasing each year by 25%. Which other colony in the Class Activity…

Suppose an experiment was conducted to compare the mileage(km) per litre obtained by competing brands of petrol I,II,III. Three new Mazda, three new Toyota and three new Nissan cars were available for experimentation. During the experiment the cars would operate under same conditions in order to eliminate the effect of external variables on the distance travelled per litre on the assigned brand of petrol. The data is given as below: Brands of Petrol Mazda Toyota Nissan I 10.6 12.0 11.0 II 9.0 15.0 12.0 III 12.0 17.4 13.0 (a) Test at the 5% level of significance whether there are signi cant differences among the brands of fuels and also among the cars. [10] (b) Compute the standard error for comparing any two fuel brands means. Hence compare, at the 5% level of significance, each of fuel brands II, and III with the standard fuel brand I. [10]

Business discuss

Chapter 4 Solutions

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 2E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 4E Ch. 4.1 - For Exercises 5-8. (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - Introduce slack variables as necessary, then...Ch. 4.1 - Introduce slack variables as necessary, then write...

Knowledge Booster

Learn more about

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

Solve the maximization problem for the investment problem in Exercise 38.

Solution Summary: The author explains how to solve the maximization problem for the investment problem in Exercise 38.

Videos

Solve the maximization problem for the investment problem in Exercise 38.

Want to see the full answer?

Chapter 4 Solutions